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 (integer)
112
Solution
<p>As C $\cap$ B $\ne$ $\phi$, c must be not be formed by {1, 2, 4, 5}</p>
<p>$\therefore$ Number of subsets of A = 2<sup>7</sup> = 128</p>
<p>and number of subsets formed by {1, 2, 4, 5} = 16</p>
<p>$\therefore$ Required no. of subsets = 2<sup>7</sup> $-$ 2<sup>4</sup> = 128 $-$ 16 = 112</p>
About this question
Subject: Mathematics · Chapter: Sets, Relations and Functions · Topic: Sets and Operations
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