Let A ={1,2,3,4,5,6,7} and B ={3,6,7,9} . Then number of elements in set { C subseteq A : C cap B ?

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1.Set Theory

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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

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