- #1
JohnDuck
- 76
- 0
Homework Statement
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.
Homework Equations
I need to prove that x*e = x and x*y = e, with x, y, e as given above.
The Attempt at a Solution
I dunno, I'm stumped. I've tried finding some sort of clever identity without any success.