Question

Let X = {1, 2, 3, 4, 5}. The number of different ordered pairs (Y, Z) that can be formed such that Y ⊆ X,Z ⊆ X and Y ∩ Z is empty , is

(A)   5² 

(B)   3⁵

(C)   2⁵

(D)   5³

Answer 1

Correct option  (B) 3⁵

Explanation :

It is given that Y ⊆ X, Z ⊆ X . Let a ∈ X . Then we have following chances that

(i)    a ∈ Y , a ∈ Z 

(ii)   a ∉ Y ,a ∈ Z

(iii)  a ∈ Y , a ∉ Z

(iv)  a ∉ Y, a ∉ Z

It is required that Y∩Z  = φ . Hence, the items (ii), (iii), (iv) above are chances for ‘a’ to satisfy Y∩Z  = φ . Therefore, Y∩ Z = φ has 3 chances for a. Thus, for five elements of X, the number of required chances is 3 x 3 x 3 x 3 x 3 = 3⁵.