If (A={1,2,3,4,5,6}), how many subsets in (\mathcal{P}(A)) have odd cardinality and contain (6)?
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Answer and explanation
Correct answer: 16
Since 6 must be included, the selected subset already has one element. To make its total cardinality odd, the selection from the remaining five elements must contain an even number of elements. Among the subsets of a five-element set, exactly 2^4=16 have even cardinality. Therefore, option B is correct.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
Since 6 must be included, the selected subset already has one element. To make its total cardinality odd, the selection from the remaining five elements must contain an even number of elements. Among the subsets of a five-element set, exactly 2^4=16 have even cardinality. Therefore, option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
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