. A is a set containing n elements
A subset P of A is chosen. The set A is reconstructed by replacing the elements of P. A subset Q of A is again chosen. The number of ways of chosen P and Q such that P ÇQ = f is
A. 22n – 2nCn
B. 2n
C. 2n – 1
D. 3n
Best Answer
Ans: D
Sol: Let A = {a1, a2, a3, . . ., an}. For ai Î A, we have the following choices:
(i) ai Î P and aiÎQ (ii) ai Î P and aiÏQ
(iii) ai ÏP and aiÎQ (iv) ai Ï P and aiÏQ
Out of these only (ii), (iii) and (iv) imply ai Ï P Ç Q. Therefore, the number of ways in which none of a1, a2, . . .an belong to P Ç Q is 3n .
Hence (D) is the correct answer.
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