. 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. 22n2nCn

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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