Question -
Answer -
Given,
A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}
(i) To verify: A ├Ч (B тИй C) = (A ├Ч B) тИй (A ├Ч C)
Now, B тИй C = {1, 2, 3, 4} тИй {5, 6} = ╬ж
Thus,
L.H.S. = A ├Ч (B тИй C) = A ├Ч ╬ж = ╬ж
Next,
A ├Ч B = {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (2, 4)}
A ├Ч C = {(1, 5), (1, 6), (2, 5), (2, 6)}
Thus,
R.H.S. = (A ├Ч B) тИй (A ├Ч C) = ╬ж
Therefore, L.H.S. = R.H.S
тАУ Hence verified
(ii) To verify: A ├Ч C is a subset of B ├Ч D
First,
A ├Ч C = {(1, 5), (1, 6), (2, 5), (2, 6)}
And,
B ├Ч 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)}
Now, itтАЩs clearly seen that all the elements of set A ├Ч C are the elements of set B ├Ч D.
Thus, A ├Ч C is a subset of B ├Ч D.
тАУ Hence verified