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  • Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that (i) A × (B intersection C) = (A × B) intersection (A × C).

Q7 (a)  Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that
             A \times ( B \cap C ) = ( A \times B ) \cap ( A \times C ).

Answers (1)

best_answer

It is given that
A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}
Now,
B \cap C = \left \{ 1,2,3,4 \right \} \cap \left \{ 5,6 \right \} = \Phi
Now,
A \times ( B \cap C ) = A \times \phi = \phi \ \ \ \ \ \ \ \ \ \ \ \ -(i)

A \times B = \left \{ (1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4) \right \}
And
A \times C = \left \{ (1,5),(1,6),(2,5),(2,6) \right \}
Now,
(A \times B)\cap (A \times C) =\phi \ \ \ \ \ \ \ \ \ \ \ \ -(ii)
From equation (i) and (ii) it is clear that
L.H.S. = R.H.S.
Hence,
A \times ( B \cap C ) = ( A \times B ) \cap ( A \times C )

Posted by

Gautam harsolia

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