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1.Set Theory
medium
Let $A =\{1,2,3,4,5,6,7\}$ and $B =\{3,6,7,9\}$. Then the number of elements in the set $\{ C \subseteq A : C \cap B \neq \phi\}$ is
A
$111$
B
$112$
C
$113$
D
$114$
(JEE MAIN-2022)
Solution
$A =\{1,2,3,4,5,6,7\} \text { and }$
$B =\{3,6,7,9\}$
Total subset of $A =2^{7}=128$
$C \cap B =\phi$ when set $C$ contains the element $1,2,4,5$
$\therefore S=\{C \subseteq A ; C \cap B \neq \phi\}$
$=\operatorname{Total}-(C \cap B=\phi)$
$=128-2^{4}=112$
Standard 11
Mathematics