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  4. 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: C ∩ B ≠ φ is

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Q. 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 _______

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Solution:

$A =\{1,2,3,4,5,6,7\}$ and
$B =\{3,6,7,9\}$
Total subset of $A =2^7=128$
$C \cap B =\phi$ when set $C$ contains the element
$1,2,4,5$
$\therefore S=\{C \subseteq A ; C \cap B \neq \phi\}$
$=\operatorname{Total}-( C \cap B =\phi)$
$=128-2^4=112$