Let A = 1 , 2 , 3 , 4 , 5 , 6 , 7 and B = 3 , 6 , 7 , 9 . Then the number of elements in the set C ⊆ A…

Given,

$A=\left\{1,2,3,4,5,6,7\right\}$ and $B=\left\{3,6,7,9\right\}$

We know that if any set has $n$ elements then total number of subset is given by $2^n$

So, total subset of $A=2^7=128$

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

$\therefore S=\left\{C\subseteq A;C\cap B\ne \varphi \right\}$

$=$ Total$-\left(C\cap B=\varphi \right)$

$=128-2^4=128-16=112$