Q.

A = {1,2,3,4,5,6,7} and B = {3,6,7,9}

Total subset of A = 2⁷ = 128

$\mathrm{C}\cap \mathrm{B}=\mathrm{\varphi }$ when set C contains the element 1, 2, 4, 5

$\begin{array}{l}\therefore \mathrm{S}=\{\mathrm{C}\subseteq \mathrm{A}; \mathrm{C}\cap \mathrm{B}\ne \mathrm{\varphi }\}\\ =\text{ Total }-(\mathrm{C}\cap \mathrm{B}=\mathrm{\varphi })\\ =128-2^4=112\end{array}$