JEE Mains · Maths · STD 11 - 1. set theory
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 \(114\)
Answer & Solution
Correct Answer
(B) \(112\)
Step-by-step Solution
Detailed explanation
\(A =\{1,2,3,4,5,6,7\} \text { and }\) \(B =\{3,6,7,9\}\) Total subset of \(A =2^{7}=128\) \(C \cap B =\phi\) when set \(C\) contains the element \(1,2,4,5\) \(\therefore S=\{C \subseteq A ; C \cap B \neq \phi\}\) \(=\operatorname{Total}-(C \cap B=\phi)\) \(=128-2^{4}=112\)
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