JEE Main · 2022 · 26 Jul 2022 · Shift 2 · Sets Relations and Functions

Let

A = {1, 2, 3, 4, 5, 6, 7}

and

B = {3, 6, 7, 9}

. Then the number of elements in the set

{C \subseteq A : C \cap B \neq = ϕ}

Answer: 112

Solution

The total number of subsets of A is

2^{7} = 128

. The subsets C of A for which

C \cap B = ϕ

are those that contain none of the elements 3, 6, 7 (the elements of B that are in A). These subsets can only contain elements from

{1, 2, 4, 5}

, giving

2^{4} = 16

such subsets. Therefore, the number of subsets C with

C \cap B \neq = ϕ

128 - 16 = 112

JEE Main · 2022 · 26 Jul 2022 · Shift 2 · Integer answer