If A has 7 elements, how many subsets in P(A) have an odd number of elements?
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Answer and explanation
Correct answer: 64
For a set with n elements, exactly half of its 2^n subsets have even cardinality and half have odd cardinality. Therefore, the number of odd-cardinality subsets is 2^(n−1). With n = 7, the count is 2^6 = 64. This includes all possible odd sizes, namely 1, 3, 5, and 7. Option B is correct.
Frequently asked questions
What is the correct answer to this question?
64
Why is this the correct answer?
For a set with n elements, exactly half of its 2^n subsets have even cardinality and half have odd cardinality. Therefore, the number of odd-cardinality subsets is 2^(n−1). With n = 7, the count is 2^6 = 64. This includes all possible odd sizes, namely 1, 3, 5, and 7. 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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