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Question 1. (12 Marks) For each of the following, determine whether it is valid or invalid. If valid, then give proof using proper, well-defined set-theoretic notation. If invalid, then give a counterexample. (a)

`(A\cap B)\cup (C\cap D)=(A\cap D)\cup (C\cap B)`

(b)

`A-(B\cup C)=(A-B)\cap (A-C)`

(c)

`A\cap CsubeA->(C-A)\cap (B-A)`

is empty (d)

`(A\cup B)-(A\cap B)=A->B`

is empty