Find a counterexample to show that the statement is false. Assume all sets are subsets of a universal set U = {1, 2, 3, 4, 5}.

Question

For all sets A, B, and C,

A ∪ (B − C) = (A ∪ B) − (A ∪ C).

A, B, C = _____

Answer 1

A = {1,2,3}

B = {4,5}

C = {4}

B-C = {5}

A U (B-C) = {1,2,3} U {5}

= {1,2,3,5}

A U B = {1,2,3,4,5}

A U C = {1,2,3,4}

(A U B) - (A U C) = { 5}

No they are not the same, so the UNION

operator U is NOT distributive over

set subtraction