Other than problem 2 being over a finite set, what is the fundamental difference in these questions (i.e. I see problem 2 has left / right cancellation properties but not sure how it changes the answer for both these questions)(adsbygoogle = window.adsbygoogle || []).push({});

Problem 1:

If G is a set closed under an associative operation such that:

Given a, y [tex]\in[/tex] G, there is an x [tex]\in[/tex] G such that ax = y, and

Given a, w [tex]\in[/tex] G, there is a u [tex]\in[/tex] G such that ua = w. prove that G is a group.

Problem 2:

If G is a finite set closed under an associative operation such that ax=ay forces x=y and ua=wa forces u=w, for every a,x,y,u,w [tex]\in[/tex] G, prove that G is a group.

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# Show G is a Group.

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