Given:

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

A × (B ∪ C) = (A × B) ∪ (A × C)

Let us consider LHS: (B ∪ C)

(B ∪ C) = {4, 5}

A × (B ∪ C) = {1, 2, 3} × {4, 5}

= {(1, 4), (1, 5), (2, 4), (2, 5), (3, 4), (3, 5)}

Now, RHS

(A × B) = {1, 2, 3} × {4}

= {(1, 4), (2, 4), (3, 4)}

(A × C) = {1, 2, 3} × {5}

= {(1, 5), (2, 5), (3, 5)}

(A × B) ∪ (A × C) = {(1, 4), (2, 4), (3, 4), (1, 5), (2, 5), (3, 5)}

LHS = RHS

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