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Prove the statements (a) and (b) using a set element proof and using only the definitions...

Prove the statements (a) and (b) using a set element proof and using only the definitions of the set operations (set equality, subset, intersection, union, complement):

(a) Suppose that A ⊆ B. Then for every set C, C\B ⊆ C\A.
(b) For all sets A and B, it holds that A′ ∩(A∪B) = A′ ∩B.
(c) Now prove the statement from part (b)

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