Answer
The statement is false. Counterexample
Let A = {1, 2, 3, 4, 5, 6}, B = {2, 4, 6, 8, 10}, and C = {1, 3, 5, 7}.
Then
A − B = {1, 3, 5},
C − B = {1, 3, 5, 7},
B U C = {1, 2, 3, 4, 5, 6, 7, 8, 10}
(A – B) ∩ (C – B) = {1, 3, 5}
and A – (B U C) = ∅
Here, we see that (A – B) ∩ (C – B) and A – (B U C) are not equal.
Therefore (A – B) ∩ (C – B) ≠ A – (B U C)
Work Step by Step
Steps:
1. Take a counterexample with some arbitrary sets A, B, and C.
2. Compute the value of (A – B) ∩ (C – B) and A – (B U C).
3. Show that these two values are not equal.