i don’t understand can someone please help?

[wild dawn]

@feral mica

what have you tried

[feral mica]

I do not know what to try i’m just lost right now.

[wild dawn]

have you learned about sets before?

[feral mica]

no this is a new topic and which i havent been taught i was just given a "ixl"

[wild dawn]

Okay..

I can try to explain a very basic idea of what sets are

[feral mica]

ok thank you

[wild dawn]

Say we have a collection of balls-- one red ball, one green ball, and one blue ball. If we want to group all these objects together, we can put them into a box

You can think of sets as a box in which you place objects

So the set corresponding to this box with these balls is {red, green, blue}

We denote sets with the curly braces, and we can label our set with a (normally capital) letter

So I could say "the set containing one red, one green and one blue ball is B = {red, green, blue}"

Does that all make sense so far? @feral mica

[feral mica]

Yes it does im starting to understand more and more i really do appreciate you helping me.

[wild dawn]

of course

So now that we understand the basic idea of sets, we can start considering sets of numbers

In that example, you're given two sets, $G = {-3,3}$ and $H = {-3,0,3,6}$.

[grizzled kestrel]

lilypad

[wild dawn]

These are different sets, because they contain different items

G is just a set of numbers, specifically -3 and 3

H is also just a set of numbers, -3, 0, 3, and 6

Do you see where it asks you to find G∪H?

[feral mica]

yes i do

[wild dawn]

The symbol that looks like the letter u is called the "set union operator"

Say we want to find a new set, L, that contains all the items from both G and H, but with no repeated elements

That is exactly what the set union does.

(i forgot to mention, each member/object/number in a set is called an element)

The set union has a special property called "commutativity" which just means that G∪H is the same as H∪G

Since H is larger, I recommend you start with that

Does the stuff I've explained so far make sense? is there anything that you need more explanation for? @feral mica

[feral mica]

when does "commutativity" come in?

[wild dawn]

commutativity, in the case of set union, is just helpful to know

it means that when we're calculating L = G∪H, we can instead to L = H∪G (which is easier to wrap your head around since H is larger)

It just means we first look at H

if your course ends up doing more set theory, you'll want to know that this set operation is commutative

[feral mica]

ohh because the order of it?

[wild dawn]

thats right

also, notice that all the elements of G are contained in H

[feral mica]

okay thats alot more sense

[wild dawn]

Let's go back to the ball example

Let's say we have another set containing a purple ball, a green ball, a blue ball and a yellow ball, C = {purple, green, blue, yellow}

Remember that B = {red, green blue}

Like I said, the set union is just taking all of the elements present in these sets, and constructing a new set from them

[feral mica]

but what if theres duplicates? in each set union

[wild dawn]

If there are duplicate elements, then we only include it once

For instance, if we want to make a new set D = B∪C, then we have D = {red, green, blue}∪{purple, green, blue, yellow}

So D = {red, green, blue, purple, yellow}

(since we only include green and blue once)

does that make sense?

[feral mica]

yes it does but one question

what if theres a negative number and a positive of the number like -1 and 1 do we include both?

[wild dawn]

yep!

those are two different numbers

so since those are unique, you include both

[feral mica]

ahh okayy!

[wild dawn]

do you have an idea for your answer for the question now?

[feral mica]

yes i think its {-3,0,3,6}

[wild dawn]

that's right, but now i'd like to ask for your reasoning

Why did you end up getting that?

[feral mica]

because i combined the set unions except the duplicates

[wild dawn]

i get what youre saying

but you only combined sets

you didnt combine "set unions"

you performed set union on two sets

does that make sense?

[feral mica]

not really what do you mean "performed"?

[wild dawn]

you did the operation of set union on two sets

Saying "i combined the set unions" is unclear because that could be interpreted as you saying that you combined two different set unions.. like (A∪B)∪(C∪D)

[feral mica]

ahh i see

[wild dawn]

i think you've got the right idea now

here's another interesting concept that they might ask you about

see how all of the elements in G are already contained in H?

[feral mica]

yes

[wild dawn]

If you have two sets A and B, where all the elements of A are contained in B

we say that A is a subset of B

And that's denoted A ⊆ B

so in that example, it turns out that G ⊆ H

[feral mica]

ohh

[wild dawn]

does that make sense?

[feral mica]

yes it does because "A" is already included into "B"

[wild dawn]

thats right

It turns out that: If we have two sets A and B such that A ⊆ B (A is a subset of B), then A∪B = B

because all the elements of A are in B

so the union of A and B will have all the elements of B without all the duplicates that are in A

so that's another way you can look at set union problems

anyways

is that question that you posted all you needed help with?

[feral mica]

well i really needed help understanding what i was looking at and you did amazing thank you so much

[wild dawn]

of course

if you have any more questions, feel free to make another thread asking. please type .close to close this thread

[feral mica]

thank you.

.close