Q. 104.0( 14 Votes )

Let A = {1,

Answer :

given: A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}

(i) To prove: A × C B × D


LHS: A × C = {(1, 5), (1, 6), (2, 5), (2, 6)}


RHS: B × D = {(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)}


Since, all elements of A × C is in B × D.


We can A × C B × D


(ii) To prove: A × (B C) = (A × B) (A × C)


LHS: (B C) =


A × (B C) =


RHS: (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)}


Since, there is no common element between A × B and A × C


(A × B) (A × C) =


LHS = RHS

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