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

Question

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

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