Question

Find a counterexample to show that the statement is fate. For all wets ( A, B ), and ( C ), if ( B cap C=A ) then ( (A-B) cap(A-C)=theta )

Answer 1

A counterexample to the given statement would be when (A-B) ∩ (A-C) is not empty.

Step-by-step explanation:

A counterexample to the given statement would be:

Let A = {1, 2, 3}, B = {2, 3, 4}, and C = {3, 4, 5}.

Since B ∩ C = {3}, and (A - B) ∩ (A - C) = {1}, the statement (B ∩ C = A) implies that ((A - B) ∩ (A - C) = θ) is true. However, in the example we provided, it is false since (A - B) ∩ (A - C) is not empty.