

InterviewSolution
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If A = {1, 2, 3}, B = {4}, C = {5}, then verify that:(i) A x (B ∪ C) = (A x B) ∪ (A x C)(ii) A x (B ∩ C) = (A x B) ∩ (A x C)(iii) A x (B – C) = (A x B) – (A x C) |
Answer» Given as A = {1, 2, 3}, B = {4} and C = {5} (i) A × (B ∪ C) = (A × B) ∪ (A × C) Let us consider the LHS (B ∪ C) (B ∪ C) = {4, 5} = {(1, 4), (1, 5), (2, 4), (2, 5), (3, 4), (3, 5)} Then, 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 (ii) A × (B ∩ C) = (A × B) ∩ (A × C) Let us consider the LHS: (B ∩ C) A × (B ∩ C) = {1, 2, 3} × ∅ = ∅ Then, 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) = ∅ ∴ LHS = RHS (iii) A × (B − C) = (A × B) − (A × C) Let us consider the LHS: (B − C) A × (B − C) = {1, 2, 3} × ∅ = ∅ Then, 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) = ∅ Thus, LHS = RHS |
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