Assume A, B, and C are all sets that lie in a common universal set.

a) Given the following statement: A (A B) = A (A B), do you think the equivalence holds? If so, prove your answer using only set identities; if not, provide ONE counter-example

b) Given A C = B C and A C = B C, can you conclude that A = B given the following statements? If so, prove your answer using only set identities; if not, provide ONE counter-example.

c) Given the following statement: (B \ A) (C \ A) = (B C) \ A, do you think the equivalence holds? If so, prove your answer using only set identities; if not, provide ONE counter-example

Hint: A \ B = A B by the definition of set minus.