(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let G be a set with an operation * such that:

1. G is closed under *.

2. * is associative.

3. There exists an element e in G such that e*x = x.

4. Given x in G, there exists a y in G such that y*x = e.

Prove that G is a group.

2. Relevant equations

I need to prove that x*e = x and x*y = e, with x, y, e as given above.

3. The attempt at a solution

I dunno, I'm stumped. I've tried finding some sort of clever identity without any success.

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# Simple proof involving groups

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