For all sets A, B, and C. Assuming each is a subset of a universal set U

Question

A) Is the following true? (A-B)∩ (C-B) = A- (B ∪C)
B) Find a counterstatement to (a)

Answer 1

(A-B) intersection (C-B) = A-(B U C), Not an identity.

counterexample:

A = {1,2,3}, B= [2], C={3}

then A-B = {1,3} C-B = {3}

A-B intersection C-B = {3}

B U C = {2,3}

A- (BUC) = {1}

or draw a Venn diagram with 3 overlapping circles