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

No. of subsets of $A=2^7=128$

$C\cap B=\varnothing \Rightarrow$no of such sub sets $=2^{4=16}$

                                              {c contains the numbers from{ 1,2,4,5}

Req . number =128-16=112