Let  $A=\{1,3,5,7,9,11\}$ and $B=\{3,7,13\}$ .Then the number of elements in the set  $\{C\subseteq A:C\cap B\ne \varphi \}$  is ________

Given $A=\{1,3,5,7,9,11\}$  and  $B=\{3,7,13\}$
Total number of subjects of  $A=2^6=64$
As,  $C\underset{\_}{\subset }A$ and  $C\cap B=\varphi$ so the set C contains only 4 elements  $1,5,9,11$
 The number of elements in the set  $\{C\underset{\_}{\subset }A:C\cap B\ne \varphi \}$
 Total number of sets-Number of sets when $C\subseteq A$and $C\cap B=\varphi$  

                                                                                                                       $=64-2^4=64-16=48$