Question

Let A = {x ∈ W | x < 2}, B = {x ∈ N | 1 < x < 4} and C = {3, 5}. Verify that

A × (B ∪ C) = (A × B) ∪ (A × C)

Answer 1

Given:

A = {0, 1} (since A = {x ∈ W ∣ x < 2}

B = {2, 3} (since B = {x ∈ N ∣ 1 < x < 4}

C = {3, 5}

B ∪ C ={2, 3, 5}

Compute A × (B ∪ C)

A × (B ∪ C) = {(0, 2), (0, 3), (0, 5), (1, 2), (1, 3), (1, 5)}

Compute A × B and A × C

A × B = {(0, 2), (0, 3), (1, 2), (1, 3)}

A × C = {(0, 3), (0, 5), (1, 3), (1, 5)}

Compute (A × B) ∪ (A × C)

(A × B) ∪ (A × C) = {(0, 2), (0, 3), (0, 5), (1, 2), (1, 3), (1, 5)}

Compare both sides

A × (B ∪ C) = (A × B) ∪ (A × C)