Originally Posted by

**BlueEagle** Hi I have a question here worth 17 marks in total. I am able to answer some of it however I am unsure where the marks are coming from:

a) State the definition of a group.

A group is a set with a binary operation which satisfies certain axioms.

A group must contain a set, binary operation and an identity element.

Im sure this might be worth 3 marks.

b) Suppose (G,~,e) is a group. Let a,b,c are elements of G and suppose that a~b=a~c

Prove that b=c stating where group axioms are being used.

All I can think of saying is that by the identity axiom and letting a=e on each side that infact b=c.