Assignment:
a) Let G be a nonempty finite set equipped with an associative operation such that for all a,b,c,d in G:
if ab = ac, then b = c and if bd = cd, then b = c.
Prove that G is a group.
b) Show that part (a) may be false if G is infinite.
Provide complete and step by step solution for the question and show calculations and use formulas.