help-0

[alpine sable]

you can get the bottom portion by adding a negative but IDK how to combine that with the top portion. any advice?

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[ember sky]

is x-2 an odd or even function

?

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[lavish cedar]

i need help ,could anyone vc since i need explain for the whole context

@crisp iron

<@&286206848099549185>

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[daring moon]

can somebody spoonfeed my little monkey brain as to how
2pi(5)^2 + pi(5 * sqrt74) combines into 5pi(10 + sqrt74)

[daring moon]

i dont know where the 5pi came from or the 10

i could see 5pi happening if the square applied to the whole of 2pi(5) because 2 squared is 4 but doesnt the square only go to the radius

[shut pewter]

I mean, by factoring out 5pi

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[daring moon]

i just dont get how it happens, sorry if im being dumb here

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[coarse hatch]

Pl help me with this

@crisp iron

[ornate condor]

um

which

oh this is a mcq

well

start with drawing a sketch mayb

[coarse hatch]

Done

@crisp iron

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[inland plank]

ok what did you try?

[spice tinsel]

I am sending now

Idk how to reduce the last step into phi^m

[inland plank]

ok

using induction is correct

[spice tinsel]

I'm stuck there

Yoooo got it

[inland plank]

but when n=2, it doesn't work, so I'm not sure if the problem is correct

oh nvm

it's correct

so you got it?

[spice tinsel]

When n=2 it does

Yes

I hope that's right

Thanku

.close

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[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

no one knows?

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@alpine sable Has your question been resolved?

[alpine sable]

<@&286206848099549185> 😭

[remote sand]

yo

im here

[alpine sable]

yo

czn you help explain a)

[alpine sable]

<@&286206848099549185>

[alpine sable]

<@&286206848099549185> ..

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

[remote sand]

at this point I think they are purposely ignoring u bro

[shut pewter]

I mean isn't kinda obvious
If Co has a lower value, it means that the decibel at that given time is also lower

That is because that Co a constant and that is something like a background noise that is accounted in the experimental data

I'm not really sure, I'm just guessing based on the graph

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[whole cargo]

Halp! How do I do the X-intercept here

[whole cargo]

This isn't from a test btw, just a reviewer

[gray isle]

quadratic formula or factorisation

ideally you'd want to first rearrange your equation into general form

[whole cargo]

Aaaah I see, the general form is the whole y = mx+b right?

Lemme try it out

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[whole cargo]

Factoring didn't work, unless I was just dumb again. Is this correct bro?

[frigid mirage]

what have you done to the quadratic formula lol

its not -b^2 inside

[whole cargo]

[frigid mirage]

it looks to me you tried to change the formula to account for the negative coefficient of x and made a mistake because of it

dont do that

or just factorize $x^2 - 5x + 6 = (x-3)(x-2)$

[ocean seal]

nebula40

[frigid mirage]

or use b = 5, a = -1 and c = -6 here

[whole cargo]

aaaaah

So that's how, ight appreciate it

.close

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[humble gazelle]

I'm not really understanding our induction step for this.

I see how he manipulates that ak+1 = 2^k(2)

but that doesn't actually make sense and I think I'm missing something

I also don't get why it's alternating an equality and inequality

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[stable basalt]

HOW DO YOU DO THIS

[lime gazelle]

Is that graph in blue for tan 2x correct?

Did we just open a channel at the same time

[stable basalt]

.CLOSE

[lime gazelle]

.close

[stable basalt]

YEH LOL

[lime gazelle]

It's not closing now

[stable basalt]

.close

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[lime gazelle]

.close

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[green oyster]

i need help with this one

[inland plank]

ok what do you have?

[green oyster]

it says to write the equation of a line that is prependicular

to y=5

and that passes through the point -7 and -5

[inland plank]

i know. what have you got so far?

any worK?

[green oyster]

y+7=5(x+5)

.close

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[torn isle]

Exact equation, and it’s differential equation

ODE

Uni Level for beginner

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[lusty trail]

im trying to check my answers for a region that satisfies three inequalities, and im using desmos, is there a way to have the region that satisfies all three be the only one shaded??

[lusty trail]

because its hard to see it

[lusty trail]

this is what i have rn

so what should i like

do

[alpine sable]

put the second and third inequalities in curly brackets

x<3\left\{y>-3\right\}\left\{y>2x\right\}

[lusty trail]

okay

thank u

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[mortal rain]

PROBABILITY
At a hockey game, Canada and the opposite team
Ck = ( Canada scores exactly k goals )
Aj = (opposite team scores exactly j goals)

They added some formulas to help with the working

a) find P(E) = ( games end in a tie ) or the probability both teams score the exact same amount of goals so k=j>=0
DONE

b) Bn = ( Canada has n goals or more ) in fonction of Ck, k>=0. Show that P(Bn) = 1/2^n
NEED HELP

c) with a property show that C = ( Canada scored an infinite amount of goals ) = 0
DONE

d) find P(M) = (Canada has scored more goals than the opposite team ) or Canada won
NEED HELP AS WELL

[mortal rain]

Huh

[lyric dock]

How to solve 1 and 2 one

[mortal rain]

I’m using this channel with my problem lol

[lyric dock]

Um

Can u tell

Me

This question is not so difficult for u i think so

[mortal rain]

I could but I’m tryna Study my own stuff lol use an other channel

[lyric dock]

Ok

Sir

[mortal rain]

.close

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[shut sleet]

could someone please help me with 1B?

[shut sleet]

you can assume the chart is correct

I was thinking that the pmf for y=1-5 is just the marginal distribution of Y (which i calculated on the right of the chart)

please @ me if you respond

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<@&286206848099549185>

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[sharp moon]

Hi!
I've a volume : 3000x3000x3000.
Inside it, multiple cubes with size 1x1x1 and with known positions.
I want to render it with a "camera" position (x,y,z). I start to render the furthest points and then the closest to the camera.
The problem is that I cannot store every cube in a list and then order it by distance because of memory limits.

I think I can solve my problem by rendering every cubes at a distance D, and then at a distance d-1, and then d-2, etc.

But... What are the coordinates of every points at a distance D from my camera (x,y,z) ? Or... Is there another solution ?

[sharp moon]

At the time, I just indexed every cubes at a distance D, and then D-1, and then D-2, etc by looping on every cubes and calculating their distance... Not the most optimised way to do it...

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@sharp moon Has your question been resolved?

[inland plank]

is this a programming question? what do you mean by "render"?

[sharp moon]

It's in a programming context, yes

but it's a math problem

[inland plank]

i think trying to get all the points at a D distance is also pretty expensive

[sharp moon]

no choice

I think

[inland plank]

is there a camera angle or something like that?

[sharp moon]

yep

but I think it doesn't change anything but which visible cubes may be rendered

For example (that's not what I want to render) : what are the coordinates of these points ?

given the middle of the sphere, its radius and the cubes size

[inland plank]

i think this is a programming question

you said you have all coordinates of the cubes right?

just store them in a hash map

with D -> point

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[final depot]

what do the vertical lines at either end of this function mean? |3𝑥−30|

[marsh rapids]

Absolute value

|x| = x if x >= 0, -x if x < 0

i.e. |x| = distance from 0 to x

[final depot]

thank you

.close

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[simple cave]

Can someone help me find the derivative of sec^2(x)

[lone heart]

Please don't occupy multiple help channels.

[simple cave]

I apply the power rule and I get 2*sec(x)

What do I do from there

[plain flame]

dont forget the chain rule

multiply by the derivative of sec(x)

[simple cave]

Why is the chain rule applied?

[plain flame]

because you have f(x) = x^2 and g(x) = sec(x)

such that f(g(x)) = sec^2(x)

[simple cave]

Ahhh ok

[plain flame]

then d/dx f(g(x)) = f'(g(x))g'(x)

[simple cave]

This is the answer

So is there an easy way to express it in terms of tan?

[plain flame]

,w 2tan(x)sec^2(x) alternate forms

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Gijs#0201

[plain flame]

doesnt look like it

[high rapids]

Gijs I have a personal question

If you don't mind

[simple cave]

This is the full question btw

[plain flame]

yeah shoot

[simple cave]

derivative of tan(x) = sec^2(x) right?

So then I just need the derivative of sec^2(x)

• the other part but I got that one

[high rapids]

Are you ask strong as the team fortress guy in your PFP?

[plain flame]

hhahah i do my best

yeah @simple cave you got it right

are you still stuck anywhere?

[simple cave]

@plain flamewelll yea, the problem is idk how to end up with 2tan(x) sec^2(x)

for the derivative of sec^2(x)

[plain flame]

chain rule

[gray isle]

power chain rule

[simple cave]

Oh wait I guess sec^2(x) = 1 + tan^2(x) right?

So they probably used that identity?

[plain flame]

dont overthink it

[simple cave]

and found derivative of that

[plain flame]

you dont need any identities

[simple cave]

then how does sec become tan?

Like, when you apply the chain and power rule how does it convert sec into tan?

[plain flame]

d/dx sec^2(x) = 2sec(x) * d/dx(sec(x))

= 2sec(x) * sec(x)tan(x)

= 2sec^2(x)tan(x)

[simple cave]

Ohh, bc the derivative of sec is sec(x)tan(x)

that's where the tan comes from

[plain flame]

yes

[simple cave]

Thanks for the help, wish me luck on my midterm in 20mjns lol

.close

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[heady pollen]

,rotate

[tacit arch]

no. it's possible

depends how you classify critical numbers, with or without multiplicity

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Please don't occupy multiple help channels.

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[vast crater]

how would you go about this?

[tall topaz]

Simplify the RHS into 1 matrix then compare each entry

[vast crater]

simplify as in add them together ignoring the a and b for now?

[tall topaz]

No multiply a and b with their respective matrix first

Then add the together

[vast crater]

uh how would you do that?

[tall topaz]

You multiply each entry by a

[vast crater]

so like 1a,3a,1a ...

[tall topaz]

Look up scalar multiplication for matrices if you’re unclear

Yeah

[vast crater]

gotcha thanks

how would you compare it?

[pallid scarab]

If you're clever you'll instantly deduce from row 1 and 3 that b = -5

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[winged rover]

why is this wrong?

the answer listed is -2-sqrt3

i would like some help on where i went wrong and what i can look to do in the future

[minor needle]

because

you've multiplied by conjugate but where is the denominator

[winged rover]

BRUHHH

NO WAY

i didnt even seee my own dummy mistake

would the denominator remain 1-sqrt3 or would it bee (1-sqrt3)(1+sqrt3)

@minor needle

[minor needle]

it would be (1-sqrt3)(1-sqrt3) = (1-sqrt3)^2

[winged rover]

and this iss beecause we multiply both top and bottom by 1-sqrt3 correct?

[minor needle]

correct

[winged rover]

and now evaluate correct?

[minor needle]

yes and simplify

[winged rover]

im going to send a picture of what i ahve

[minor needle]

u can simplify it further, take out (-1) then multiply by conjugate again

basically rationalizing the denominator

[winged rover]

alright got it

but now im confused at the end

i still have the -1 outside of the bracket

will i have to multiply it into the whole thing or just the first term

sending pic now

@minor needle

[minor needle]

yes

it's correct

[winged rover]

so i leave the negative 1 outside

and just take away the brakets?

i dont have to multiply it into 2-sqrt3 ?

making it -2+sqrt3

[minor needle]

ah, I spot your mistake

[winged rover]

the - doesnt become a + ?

[ocean seal]

Modus

[winged rover]

i see

it only takes the - away from the numerator

[minor needle]

generally

$$\frac{-a}{b}=\frac{a}{-b}=-\frac{a}{b}$$

[ocean seal]

Modus

[minor needle]

you can put "-" wherever you want

[winged rover]

i see

thanks so much Modus

.clos

.close

[lone heart]

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[severe mural]

How would this work 🤔 (15)

[lone heart]

@severe mural Has your question been resolved?

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[rancid wolf]

could someone help me

[rancid wolf]

could somone help me

#real-complex-analysis

[raw grotto]

Yes

See point y

[rancid wolf]

yea

[raw grotto]

-2 -5

Make it 2, -5

[rancid wolf]

lemme say what im stuck on rq

[raw grotto]

Then add 2 to x minus 4 to y

[rancid wolf]

im confused

[raw grotto]

0 -9

Is new point y

Do same for all

[rancid wolf]

so

the coordinates + x

[raw grotto]

4 -9*

Opposite of x cordinate

Since it is across y axis

[rancid wolf]

the coordinates i have is

3, -9

3, -5.5

-5,-2

-5,-9

@raw grotto

am i wrong

[raw grotto]

Yes

See blue is right

Just move each blue point right 2 down 4

And trace those points

[rancid wolf]

so i didnt need to rotate?

[raw grotto]

No

You did

Do it from the blue points

2 steps

Rotate

Then move rotated shape

[rancid wolf]

yea i rotated from the blue point thats what i got from it

[raw grotto]

Why you rotating blue points

[raw grotto]

Oh i didnt read first image

[rancid wolf]

yea

so is purple right

[raw grotto]

Yes

[rancid wolf]

ok ok

so do i do +2 -4 on the new rotated coordinates

[raw grotto]

Then translate

Yes

[rancid wolf]

when i do it to the -9

i get

-13

im confused

thinking i went to high

and my calculations are wrong

@raw grotto

am i right on that?

[raw grotto]

The graph is bad just imagine point

And plot

[rancid wolf]

ok

thank you

for your help kevin durant

favorite basket ball player

mvp im tellin you

[raw grotto]

Yes mvp

Im 🐐

[rancid wolf]

my final coords are

5, -13

5, -9.5

-3, -6

3, -13

are those right?

@raw grotto

[raw grotto]

9.5???

[rancid wolf]

-5.5 - 4

[raw grotto]

Oh

Yes good

[rancid wolf]

Better than LeLongevity?

w mans

love you bro

[lone heart]

@rancid wolf Has your question been resolved?

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[hexed hawk]

hi

[hexed hawk]

There is a king in the hand or there is an ace in the hand, or both. There is a queen in the hand or there is an ace in the hand, or both.

If only one of these assumptions can be true, which is more likely to be in the hand: the king or the ace?

[inland plank]

depends on which one has a higher probability

if the second one has 0% probability, and from the first one, if king and ace have the same probability, 50%

otherwise, ace has higher probability

[hexed hawk]

ik its the king bc he explained it a long time ago

i just dont know how

it's just this question straight up nothing more

[inland plank]

i don't believe king has higher probability

[hexed hawk]

that's what he said

butif udont think so, conceptually why not

[rose sigil]

conceptually it's because only one is true means the other one is false (and I mean that's why the king is more likely)

[hexed hawk]

what? it is like

[slate jolt]

basically it says that P(1 and 2) =0 right?

[hexed hawk]

no its like

(KvA)

(QvA)

but the thing says

(KvA)⊕(QvA)

because v is or inclusive which could be both

⊕ is exclusive where it is either or

so in either hand u can have an ace

its just not asking abt the queen

[slate jolt]

theres only one hand no?

[hexed hawk]

like the probability of both (KvA) and (QvA) happening at the same time?

yes but you dont know which is

the hand could either be (KvA) or (QvA)

[slate jolt]

you know both cant happen at the same time

so those two events are disjoints

[hexed hawk]

(KvA)⊕(QvA)

[slate jolt]

or their intersection is empty

[inland plank]

yeah, as others said, the probability of picking an ace is 0

(I was wrong initially)

[hexed hawk]

that doesnt make sense tho

because it could be a king OR an ace, or both

both implies you could have both

or just ace

even if just one of the assertions was true

[inland plank]

yeah but it said only one of the assertions is true

which means the other assertion is false

[slate jolt]

P((KuA)n(QuA))=0 given only one can be true

[hexed hawk]

yes so lets say the first one is

you can still get an ace in the first assertion

KvA is or inclusive

[inland plank]

no, because assertion B is false, so ace cannot be drawn

[slate jolt]

but A is included(KuA)n(QuA)

[hexed hawk]

what is telling u assertion b is false

even if it is false then the true assertion is: there is either a king in the hand or an ace or both

[inland plank]

if assertion a is true, assertion b is false, from the problem's condition

[hexed hawk]

yes but how do u know assertion a is true it says nothing about that though

[inland plank]

that's a true assertion yes, but from b's falseness, ace cannot be drawn

[hexed hawk]

they're independent assertions

[inland plank]

because you said so

[hexed hawk]

because of what youre sayign

like if you had to literally explain why the king, why

but you could possibly draw an ace

[inland plank]

because king can be chosen, but ace cannot be chosen ever

[hexed hawk]

the second assertion has nothing to do with the first one

theyre just two proposed ones

[inland plank]

i know, but the problem states that ONLY one of the assertion can be true

[hexed hawk]

yes exactly

[inland plank]

meaning if assertion B is true, assertion A is false

[hexed hawk]

so in the assertion 2 (QvA) is false, erase it entirely

so

ONLY FROM

1. There is a king in the hand or an ace, or both

why king?

[inland plank]

ok, let's forget all that and just focus on one thing

if assertion A is false, what does that mean?

[hexed hawk]

that B is ttue

this tho

[inland plank]

yeah, but let's forget about B too

let's focus on assertion A, and try to understand what assertion A is false means

[slate jolt]

heres the full proof

[inland plank]

yeah, formulas are nice but understanding conceptually is easier

[hexed hawk]

the => states: Probability(K or A) and (Q or A) = 0

what is A C

[slate jolt]

A included in (...)

[hexed hawk]

?/

the ace?

[slate jolt]

events are sets

A is the event "the ace is in the hand"

[hexed hawk]

in your formula what does A represent

bc in class A represents concusions

(sigma|A) premises|conclusion

[slate jolt]

i re used your notations

[hexed hawk]

A is ace

(KvA) means King or Ace, or both

(QvA) means Queen or Ace, or both

[slate jolt]

yeah right

[slate jolt]

as i said

[hexed hawk]

what is this

[slate jolt]

inclusion

K is the event "the king is in the end"

[hexed hawk]

?

ive never heard someone use that

is it

⊃

[slate jolt]

it is

[hexed hawk]

which is like

[slate jolt]

but the other way around

[hexed hawk]

A ⊃(KvA) meaning Ace, then K or A

[slate jolt]

to clear things out

we are doing probabilities here not logic

[hexed hawk]

this is a logic course

[slate jolt]

even though those are somewhat related

[hexed hawk]

so the symbols ive been using is logical connectives and stuff

⊃ --- then

≡ --- iff

[slate jolt]

ok so lets write a logic proof then

[hexed hawk]

this isnt one?

¬ -- not

[inland plank]

@hexed hawk we know what "assertion A is true" means: King or Ace or both are in the hand. can you just state what "assertion A is false" means?

that will make things much easier to understand

[hexed hawk]

Assertion A is false would mean that in that scenario there isnt a king in hand or an ace in hand

[inland plank]

right

so if B is true, it means A is false, thus "there isnt a king in hand or an ace in hand" right?

[hexed hawk]

but but but

why are we assuming A is false and not B

[inland plank]

there are only two cases, A true and B false, and A false and B true

we just took one case

[inland plank]

don't look at the formula. think about it conceptually. it's REALLY EASY

[hexed hawk]

why is there a scenario with two aces

[inland plank]

ok i give up

[slate jolt]

wdym?

thats not what i wrote

[hexed hawk]

conceptually is good to start w

[inland plank]

yeah, then stop looking at the formula and stick with me for 5 minutes

[slate jolt]

the first line corresponds to "KvA and QvA cant happen both at the same time"

but yeah try following

[inland plank]

otherwise, i'll mute this channel and see other channels thx

[slate jolt]

the conceptual part

[hexed hawk]

kkkkkkk

[slate jolt]

i thought formula could help since you were stubborn with your way of seeing things

[hexed hawk]

it's hard not to be stubborn if it is just stated and not explained if that makes sense

smh rules of logic is shaking its head antiguerrilla

[slate jolt]

basically either 1) is true and 2) is false

or the opposite way

[hexed hawk]

LMFAO IT AUTOCORRECTED astaghfirullah to antiguerrilla

[hexed hawk]

yes but like... explain why no ace

[slate jolt]

yeah

let me get to it

so lets do the first case

then we'll do the second case

assume 1) is true and 2) is false

so we know

KvA is true

[hexed hawk]

yuh

[slate jolt]

QvA is false

but since QvA is false

that means

Q and A are false

since if one of the 2 were true

QvA would be true

[hexed hawk]

So, why does the falsehood of A in the second assertion leak into the first assertion

[hexed hawk]

i got everything else but this

and then QvA being true if u just said its not

[slate jolt]

its a justification

to say Q and A are false

because if Q is true, QvA is true which as you said its not

so Q is false

and same reasonning with A

[hexed hawk]

but can we not assume that one is true over the other, because initially u start out not knowing

bc we are doing hypotheticals that one is true and the other is not rn

which only one is true

[slate jolt]

wdym? about Q and A?

[hexed hawk]

but why do we start off choosing a wrong one

[slate jolt]

we do both cases

[hexed hawk]

but it is not making sense

just like straight up

why would QvC be false

over KvC

[slate jolt]

we dont know

[hexed hawk]

then like

[slate jolt]

but we do both cases

[hexed hawk]

what is the point of the question

do both cases and then combine the answers/

?

[slate jolt]

first we imagine that one is true and not the other, we draw conclusions

and then we imagine the opposite and we draw conclusions

and since we drew the same conclusion in both cases

that means whichever it is

[hexed hawk]

if KvA is true, isnt it an equal chance?

[slate jolt]

the conclusions still hold

if you only knew that yeas

but we also know that if KvA is true

QvA is false

right?

[hexed hawk]

yea

but ok so look

1. If we assume KvA is true, then its more likely to be the queen.

[slate jolt]

why,

?

[hexed hawk]

2. If we assume QvA is true, then its more likely to be the queen

[slate jolt]

oh ok

you are imagining

yeah go ahead

[hexed hawk]

because then the falsified assertion cancels out the ace

whcih doesnt make sense to me

but yall both said that

bc it doesnt say that components of one assertion is canceled out by the falseness of it in another one

1. If we assume KvA is true, then its more likely to be the king.

2. If we assume QvA is true, then its more likely to be the queen

[slate jolt]

wdym?

[hexed hawk]

in your guys' logic bc u keep saying ace is impossible but not why

[slate jolt]

since i started explaning after the formulas i didnt state once Ace is impossible

[hexed hawk]

thats what yall have been saying

or just stating this is the answer

but not w h y

[slate jolt]

i'm trying to explain

and then mid explanation

[hexed hawk]

aii then go and say when ure done lol

[slate jolt]

you say im not explaninig

[hexed hawk]

its not giving an explanation tho

continue continue

[slate jolt]

so do i need to recap where i was at?

or did you follow

[hexed hawk]

recap rq

[slate jolt]

we dont know which of KvA and QvA is true

so we do two cases

one where KvA is true and Qva is false

and after that

we do the case where KvA is false and QvA is true

right?

so lets do the first case

[slate jolt]

we know given this that QvA is false

so if you apply negation

Not(QvA) is true

so (not(Q) and not(A) )is true by distributing the not

and then this means not(A) is true

which is the same as A is false

so in the first case we arrived to A is false

IN THIS CASE, did something bother you?

next i'll do the other case

[hexed hawk]

so int this case: the falseness of A in (QvA) translates to the falseness of A in (KvA)?

[slate jolt]

oooh so thats your issue

theres a reason why A is the same variable in both assertions

we wrote it like this because its the same thing

if i write 2=3-1 and 2 = sqrt(4)

those are the same

and indeed

[hexed hawk]

u right u right

[slate jolt]

3-1=sqrt(4)

if they were issues with this

you should not have named the same

[hexed hawk]

but like is there is a reason that they are the same variable and influence eachother, or just the nature of the question

[slate jolt]

its just how we interpreted what was said

A is ="there is a ace in the hand"

if you want an assertion that can be true or false

and indeed KvA is "there is an ace or a king in the hand"

"there is an ace or a king in the hand" = "there is a ace in the hand" or "there is a king in the hand"

"there is an ace or a queen in the hand" = "there is an ace in the hand" or "there is a queen in the hand"

so yeah they're the same

but we didnt even need it

to prove A is false

[hexed hawk]

why so

[slate jolt]

where did i use it?

[hexed hawk]

for this

like we don't need that info to prove A is false, so what do we use

[slate jolt]

re read this part, i only talk about QvA

[hexed hawk]

Then in the case of KvA being true, because ~A in (QvA), it also made the A in KvA false.... for some reason bc theyre the same varibale

that is my understanding

[slate jolt]

yeah thats also true

its not for some reason,

we need to redo the set up i think

lets call A = "there is a ace in the hand"

its an assertion

that is either true or false

the same with K and king, Q and queen

[hexed hawk]

or is it like

[slate jolt]

like what?

[hexed hawk]

if we represent the entire thing like this

(KvA)⊕(QvA)

then have the case of (KvA) being correct

then it could be changed to

(KvA)&(~Q&~A)

nvm

that doesnt make sense

[slate jolt]

so given this setup

we can interpret the two things said

as KvA

and QvA

notice these two talk about the same A

and if you have a problem with that it should be dealt with right at the beginning

even though here there are none

[hexed hawk]

none what

[slate jolt]

by calling the two variables different

no problems

[hexed hawk]

since theyre not, they must be categorized as the same

[slate jolt]

there are*

?

[slate jolt]

what are they not?

but this whole issue i think is very weird

[slate jolt]

because you have no problem writing this

where you use the supposedly two different As

in the same expression

with the same notation

[hexed hawk]

bc the question is sentences in my head LOLLL

[slate jolt]

yeah this is why we do maths, to calm things down put it on paper

and have tools to think about things and hopefully get less confused

can you understand the formal proof i gave?

[hexed hawk]

ok ok so we have that written above, same A

[slate jolt]

or the first case proof?

[hexed hawk]

this?

[slate jolt]

yep

[hexed hawk]

line 1: (king or ace) and (queen or ace) = false....... line 2: (king and ace) or (queen and ace) or (ace and king) or (ace and ace) = false this im like ??????????????...................line 3: not(King and Queen) and not(queen and ace) and not(king and ace) and not(ace)=true.................. not(ace) is true.... (ace) is false

[slate jolt]

negation

[hexed hawk]

ah ok ok

[slate jolt]

so the line 1 to line 2 is simply expanding / distributing

the brackets

[hexed hawk]

i know what it all says

understand no connection nor implication

besides for line 1

[slate jolt]

wdym?

[hexed hawk]

ace or ace is 100% false bc thats not even an option

but then u have two scenarios of king/ace

[hexed hawk]

like i can decipher what the proof is saying

but dk what it means

[slate jolt]

this is a formal proof

[hexed hawk]

ik that

[slate jolt]

when writing it you should not think about what each line means

but if the formal rules of logic are respected

and if so,

[hexed hawk]

no idea

i have no idea how to do derivations

[slate jolt]

how are you supposed to do this exercise then?

even what i used in my case by case proof is the same kind of thing

you need to know how to manipulate logic expressions

[hexed hawk]

and also even with the (KvA)⊕(QvA) that represents the scenario i have no idea how to get from that to answer... esp derivations

[hexed hawk]

trying to understand thts why i put it in the chat

[slate jolt]

no but there are two different things,

understanding whats happening in this specific case

[hexed hawk]

this feels like circles around what an answer would be tho

[slate jolt]

which can be hard if you think of it the wrong way at first

and theres also, knowing what you are allowed to do with logic assertions

and what you are not

and why

[hexed hawk]

but your proof

why would u put the scenario of (ace and ace) together

bc thats not a situation presented by the question

like if u were to write out your answer to the question entirely, conceptually and formula wise... how would u do it

maybe we work backwards from that

[slate jolt]

either i would do a formal proof

which as i said

[hexed hawk]

i have like the modus tollens and substitution rules in mind

[slate jolt]

isnt meant to be understood conceptually

but just a game on rules of logic

to get to the answer

[hexed hawk]

but how does ur formal proof reflect the question

dont u need to put

[slate jolt]

or i would do a conceptual proof by doing the two cases

[hexed hawk]

this is bc rule modus tollens or

DeMorgan or whatever

[slate jolt]

oh i can do that

but i dont know all of the names of the rules

[hexed hawk]

son just smart like dattt

but again why (ace and ace)?

[slate jolt]

theres no why

[hexed hawk]

mood

[slate jolt]

its just the result i get from applying something

i use the rule

[hexed hawk]

applying a rule?

[slate jolt]

that you can distribute

[hexed hawk]

wouldnt it be like

[slate jolt]

"or" and "and"

in a logic expression

[hexed hawk]

(~A^A)

[slate jolt]

like (A or B) and (C or D) <=> (A and C) or (A and D) or (B and C) or (B and D)

and doing this

i arrive to line 2

like its the same if i had

a(2x+b)=3

[hexed hawk]

so is this for the entire question or one scenario of a specific assertion being assumed true

[slate jolt]

this is the entire question

[hexed hawk]

ok w these rules

for each line

what did u use

maybe ill understand better

[slate jolt]

line 1 to 2

distribution

[hexed hawk]

crazy to me how logical proofs is not meant to be understood conceptually lololol

[slate jolt]

it is

but once you understood that the basic rules are true

you can carry on calculations

and be assured that they are true

without caring about what they mean

and thats why they are useful

because you can abstract yourself

[hexed hawk]

ah okok

[slate jolt]

transform the conceptual problem

into a maths problem with a set of rules

which is supposedly easier to deal with

since you know the rules

[hexed hawk]

from line two (which is [K^Q]v[Q^A]v(A^K....) to line three?

maybe easier to see

[slate jolt]

basically it says that x =False is the same as not(x)

line 2 to 3 is the definition of Not i guess

[hexed hawk]

https://tenor.com/view/bunnies-what-confused-meh-gif-13712192

[hexed hawk]

but which rule would back that up

modus tollens, negation intro, disjunctive syllogism, DeM, Definition of a Conditional?

[slate jolt]

basically its not written in here because the way of writing logic assumed here

doesnt allow for x=False

instead we just say not X

[hexed hawk]

whats x

[slate jolt]

x is any statement

[hexed hawk]

i mean rn rn

[slate jolt]

oh x is

like formally i shouldnt be writing

something = False

but rather

Not(something)

[hexed hawk]

i dont get what this means tho bc it doesnt make sense in my head compared to the word problem

[slate jolt]

its a logic statement

[hexed hawk]

so how would u properly write it out then

where does A^A come from

did u mean (Q^A)?

[slate jolt]

i'm writing it all wait a bit

[hexed hawk]

okie dokey!

[hexed hawk]

ok ok ok

definition of that thing is or but not both

[slate jolt]

there are two different definitions

A XOR B is

(A and Not(B)) or (Not(A) and B)

[hexed hawk]

huhh no no we learned

PvQ is inclusive or

the P (symbol thing) Q is exclusive or

[slate jolt]

yeah right

[hexed hawk]

so no both

only P or Q

first one is P or Q or both

[slate jolt]

isnt exclusive or this?

let me finish please

[slate jolt]

if you apply double negation to this

Not[ Not [(A and Not(B)) or (Not(A) and B)]]

we apply morgans law on the first

let me write it 2 sec its too hard on keyboard

[hexed hawk]

kkkkk

are u explaining what u just sent \

bc idk where this came from

[slate jolt]

i'm trying to explain to you the definition i used for exclusive or

because you seemed to not accept it

basically what it says is

A XOR B is :

[hexed hawk]

(brb oneee sec)

[slate jolt]

not (A and B) and not (not(A) and not(B))

which is the same as not [ (A and B) or (not(A) and not(B)) by morgans law

then not [(A and B) or not(A or B))] still by morgans law

https://en.wikipedia.org/wiki/Exclusive_or#Equivalences,_elimination,_and_introduction

[hexed hawk]

this is the same as what i said

P or Q, but not both

[slate jolt]

w/e just read this, my definition is the same as 4th one

there are many ways to write exclusive or

[hexed hawk]

im so confused what youre talking abt rn lmfao what other way did u say it

simpliest definition

P or Q, not both

overall, that is what it is right

[slate jolt]

yeah

but what i used

is

not Both and not none

which is the same as yours

[hexed hawk]

so conjunction elimnation is for the second most line to the third?

[slate jolt]

yeah

[hexed hawk]

period

so this entire proof just says

proves

~A, as in an ace wouldnt be more probable than a king

[slate jolt]

as ace is impossible

not (A) is litterally

not "the ace is in the hand"

[hexed hawk]

ok ok

and not ace in the hand

means

that the king is more probable still

[slate jolt]

yeah

[hexed hawk]

because probability of ace is 0%

[slate jolt]

the king cant be less probable than 0

yeah

[hexed hawk]

ok ok ok i can understand more from seeing the rules

[slate jolt]

what the other person was trying to convey

is that in this case

[inland plank]

it's not 0%. it's an impossible event. 0% is not totally impossible

[slate jolt]

you can do a conceptual reasoning

[slate jolt]

yeah but thats enough

they ask which is more probable

[hexed hawk]

have u been watching this process the whole time? 😮

patience

ok ok ok ok

i understand now thank you

[slate jolt]

i dont think its time to introduce probabilities nuances

logic is enough

but the other proof of case by case is actually more insightful

for understanding whats actually happening

[inland plank]

not really. muted for 15 minutes and it popped up. you guys are so patient lol

[slate jolt]

the one i did is more useful to learn how to manipulate assertions

[hexed hawk]

i was gonna say damn

[hexed hawk]

that has the substitution rules and inference rules

?

if you have the want or time

what do u think about this problem

I think the professor said 3 cards. Obviously you need to flip 5 and 2, because if they have anything other than a letter before M it violates the rule. But what is the third card and why?

I would say X and Z are irrelevant bc the rule says only what a number less than or equal to 5 must correspond w?

noidea

the wason selection test is usually 4 cards soooo tf

[slate jolt]

set things up

dont try to reason right off the bat

[hexed hawk]

ok ok ok

[slate jolt]

A(c) = " card c has a number less or equal to 5 on one side"

B(c) = " card c has a letter that comes before M in the alphabet"

then how does the quoted sentence translates

in terms of A and B?

[hexed hawk]

i have no idea

[slate jolt]

if A then B

or A => B

[hexed hawk]

there is no if then tho

[slate jolt]

yeah

[hexed hawk]

in this

if it was

[slate jolt]

i introduce it right here

i broke it down

[hexed hawk]

Rule: Card with a number less than or equal to 5, has a letter coming before M on the alphabet on the other side

then

A=>B i could see

[slate jolt]

ok

[hexed hawk]

wats the A(c) the c in this