JEE MAIN - Mathematics (2022 - 26th July Evening Shift - No. 15)
Let $$A=\{1,2,3,4,5,6,7\}$$ and $$B=\{3,6,7,9\}$$. Then the number of elements in the set $$\{C \subseteq A: C \cap B \neq \phi\}$$ is ___________.
Answer
112
Explanation
As C $$\cap$$ B $$\ne$$ $$\phi$$, c must be not be formed by {1, 2, 4, 5}
$$\therefore$$ Number of subsets of A = 27 = 128
and number of subsets formed by {1, 2, 4, 5} = 16
$$\therefore$$ Required no. of subsets = 27 $$-$$ 24 = 128 $$-$$ 16 = 112
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