JEE Main · 2012 · 29 Apr 2012 · Offline · Sets Relations and Functions

Let

X = {1, 2, 3, 4, 5}

. The number of different ordered pairs

(Y, Z)

that can be formed such that

Y \subseteq X, Z \subseteq X

and

Y \cap Z

is empty, is

Answer: (B)

Solution

Build the pair

(Y, Z)

one element at a time. For each of the five members of

X

there are three allowed outcomes that keep

Y

and

Z

disjoint: the element goes into

Y

alone, into

Z

alone, or into neither; placing it in both is forbidden. These choices are independent across the five elements, so the number of ordered pairs is

3^{5}

JEE Main · 2012 · 29 Apr 2012 · Offline · Single correct option