Check My Proofs

[pastel adder]

Could someone check these proof please? i'm self studying discrete mathematics so i have no teacher or classmate to check for me.

[molten bramble]

Your counter example for symmetry in the first proof doesn’t work, since neither (2,3) nor (3,2) are in R.

What you need is some (a,b) in R such that (b,a) is not in R.

[cloud trail]

you should still get a teacher to check for you, Teachers are important and can give u tips and better than just relying on yourself, when you finish college then you stop

[pastel adder]

ahhh ok

[pastel adder]

hopefully, i'll be starting uni the coming academic year

but i'm unable as of yet

[pastel adder]

i changed the last \in into \notin.

so $15 \nmid 3 \notin Z$

[west summit]

Arch

[molten bramble]

The example is good.
I don't know how the notation $a|b$ is defined for you but in general it isn't defined such that $a | b$ is a number, so I wouldn't say that those are elements of $\mathbb{Z}$.

[west summit]

Azyrashacorki

[pastel adder]

i'll change it. thanks

[molten bramble]

It's sufficient to say that $3 | 15$, so $(3,15) \in R$ but $15 \not | 3$

[west summit]

Azyrashacorki

[molten bramble]

And as a nitpick, your last line should read more like "It is not true that for all $a,b \in \Z$, if $a | b$, then $b | a$".

[west summit]

Azyrashacorki

[molten bramble]

Or something along those lines.

[pastel adder]

i think the reader can clear infer that 1/5 \notin Z haha

[molten bramble]

Seems good. Again there's the slight mismatch in type for the | notation.
In general a | b, which you can read as "a divides b," is not an operation. It's just shorthand for the statement that b = ka for some integer k. I can understand what you mean as 3 | 15 = 5, but a|b is something that is True or False, not a number.

[cloud trail]

very well, just make sure you know why you dont want a teacher to check if you think you are ready not if u think you are too smart for it

[pastel adder]

ahhh, i see. I'll change that

[molten bramble]

I get what they mean and yes it's ideal to follow some course and have some means of getting your work assessed to see whether what you're doing is correct. However you've mentioned you're not in uni yet, so I would say it's good to try and get the hang of those things in advance, even if by yourself, especially with how much is available online nowadays (full courses for instance).
In the meantime, starting to get the hang of proofs is a very useful tool ahead of university, and if anything you can further their understanding by taking a relevant course when you get there.

In any case, don't hesitate to ask for help here or elsewhere should you need it.

[pastel adder]

thanks. I have to follow a discrete mathematics course at Open University. If i pass this course, i'll have shown that i'm disciplined in learning so i can get into Uni. This is an unusual path, but i have to do this in order to get into Uni without a highschool diploma.

and then i have to pass another test in order to actually get permission to sign up for uni

[molten bramble]

You got this!

[pastel adder]

.solved