Let A = {1,2,3,4,5,6,7} and B = {3,6,7,9}. Then the number of elements in the set $\left\{C\subseteq A:C\cap B\ne ?\right\}is............$

<p>&nbsp;<math><mrow><mi>C</mi><mo>⊆</mo><mi>A</mi><mtext> </mtext><mtext> </mtext><mi>a</mi><mi>n</mi><mi>d</mi><mtext> </mtext><mtext> </mtext><mi>C</mi><mo>∩</mo><mi>B</mi><mo>=</mo><mi>φ</mi></mrow></math></p><p>If C is formed only by {1, 2, 4, 5} total number of subsets of A = 27.</p><p>Total number of subsets of {1, 2, 4, 5} = 24</p><p><math><mrow><mo>∴</mo></mrow></math>&nbsp;Number of subsets where&nbsp;<math><mrow><mi>C</mi><mo>∩</mo><mi>B</mi><mo>≠</mo><mi>φ</mi></mrow></math></p><p>= 27 – 24 = 112</p>

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