please help prove this abstract algebra..?

Question

suppose that * is an associative and commulative binary operations on a set S, show that H = {a element s such that a * a = a} is closed under *

* means asteris as the binary operation...

Answer 1

Let a and b be 2 elements in H. Then we have to
show a*b is also in H.
So look at (a*b)*(a*b).
By the associative law, this is
a(b*a)*b
and the commutative law gives
a(b*a)*b = a*a*b*b = a* b.
So H is closed under *.

Answer 2

properly, you need to and you need to not. a working laptop or computer is a logical device, the subject is it demands a software written by way of people to offer it the sequence of logical steps mandatory to remedy a difficulty. i'm not saying it is not plausible to jot down a software to hunt for proofs of particular theorms, yet in many circumstances in case you need to write that software you in all risk ought to arise with the evidence your self without wanting this technique .

Answer 3

I think that Josh J means that this question, as stated, is gibberish, and not capable of being answered. You will need to rewrite it much more clearly before it can be understood.