Question

A is a set containing n different elements, a subset P of A is chosen at random. The set A is reconstructed by replacing the elements of P and a subset Q of A is chosen at random. The number of ways of choosing P and Q so that P Č Q = A is

• A. 2ⁿ
• B. 3ⁿ
• C. 4ⁿ
• D. ⁿC₂. 2ⁿ

Answer 1

Answer: (B)

3ⁿ

Answer 2

Let a Ī A, then we have the following possibilities for the event P Č Q = A

(i) a Ī P, a Ī Q

(ii) a $\notin$ P, a Ī Q

(iii) a Ī P, a $\notin$ Q

each element can be selected in 3 ways.

\ total number of ways = 3ⁿ