Question

If A = {-2, 0, 1, 3, 5}, B = {-1, 0, 2, 5, 6} and C = {-1, 2, 5, 6, 7}, then show that A – (B ∪ C) = (A – B) ∩ (A – C).​

Answer 1

Answer:

A = {-2, 0, 1, 3, 5},

B = {-1, 0, 2, 5, 6}

C = {-1, 2, 5, 6, 7}

B ∪ C = {-1, 0, 2, 5, 6, 7}

A – (B ∪ C) = {-2, 1, 3} … (1)

(A – B) = {-2, 1, 3} (A – C) = {-2, 0, 1, 3}

(A – B) ∩ (A – C) = {-2, 1, 3} … (2)

From (1) and (2), it is verified that A – (B ∪ C) = (A – B) ∩ (A – C)

Answer 2

Answer:

A = {-2, 0, 1, 3, 5}, B = {-1, 0, 2, 5, 6} and C = {-1, 2, 5, 6, 7}, then show that A – (B ∪ C) = (A – B) ∩ (A – C).