If (|A|=7), how many subsets in (\mathcal{P}(A)) have even cardinality?
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Answer and explanation
Correct answer: 64
For every nonempty finite set with n elements, exactly half of its 2^n subsets have even cardinality and half have odd cardinality. This follows by pairing each subset with the set obtained by toggling one fixed element. Here n=7, so the number of even-cardinality subsets is 2^7/2=2^6=64. Option B is correct.
Frequently asked questions
What is the correct answer to this question?
64
Why is this the correct answer?
For every nonempty finite set with n elements, exactly half of its 2^n subsets have even cardinality and half have odd cardinality. This follows by pairing each subset with the set obtained by toggling one fixed element. Here n=7, so the number of even-cardinality subsets is 2^7/2=2^6=64. 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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