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                                    Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that1. A × (B ∩ C) = (A × B) ∩ (A × C)2. A × C is a subset of B × D | 
                            
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Answer»  1. A × (B ∩ C) ={1, 2} × Φ = Φ A × B = {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (2, 4)} A × C = {(1, 5), (1, 6), (2, 5), (2, 6)} (A × B) ∩ (A × C) = Φ Hence; A × (B ∩ C) = (A × B) ∩ (A × C) 2. A × C = {(1, 5), (1, 6), (2, 5), (2, 6)} B × D = {1, 2, 3, 4} × {5, 6, 7, 8} = {(1, 5), (1, 6), (1, 7), (1, 8), (2, 5), (2, 6), (2, 7), (2, 8), (3, 5), (3,6), (3, 7), (3, 8), (4, 5), (4, 6), (4, 7), (4, 8)} Hence A × C is a subset of B × D.  | 
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