Let A={1,3,5,7,9,11} and B={3,7,13} .Then the number of elements in the set {C⊆A:C∩B≠ϕ} is _______

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

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answer is 48.

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Detailed Solution

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