Let A = {1, 2, 3, 4, 5, 6, 7} and B = {3, 6, | vedclass

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(B) Given $A = \{1, 2, 3, 4, 5, 6, 7\}$ and $B = \{3, 6, 7, 9\}$.Total number of subsets of $A$ is $2^{|A|} = 2^7 = 128$.We want to find the number of

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$112$

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(B) Given $A = \{1, 2, 3, 4, 5, 6, 7\}$ and $B = \{3, 6, 7, 9\}$.Total number of subsets of $A$ is $2^{|A|} = 2^7 = 128$.We want to find the number of subsets $C \subseteq A$ such that $C \cap B 
eq \phi$.This is equal to the total number of subsets of $A$ minus the number of subsets $C \subseteq A$ such that $C \cap B = \phi$.$C \cap B = \phi$ means $C$ must be a subset of $A \setminus B$.$A \setminus B = \{1, 2, 3, 4, 5, 6, 7\} \setminus \{3, 6, 7, 9\} = \{1, 2, 4, 5\}$.The number of such subsets $C$ is $2^{|A \setminus B|} = 2^4 = 16$.Therefore,the number of subsets $C \subseteq A$ such that $C \cap B 
eq \phi$ is $128 - 16 = 112$.

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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