Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} and A be the set of odd elements of U. How many 3-element members are there in P(A')?
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Answer and explanation
Correct answer: 20
The odd elements form A = {1, 3, 5, 7, 9, 11}, so the complement A' consists of the six even elements {2, 4, 6, 8, 10, 12}. Members of P(A') are subsets of A'. The number of members containing exactly 3 elements is the number of ways to choose 3 elements from 6, namely C(6,3) = 6!/(3!3!) = 20. Thus option C is correct.
Frequently asked questions
What is the correct answer to this question?
20
Why is this the correct answer?
The odd elements form A = {1, 3, 5, 7, 9, 11}, so the complement A' consists of the six even elements {2, 4, 6, 8, 10, 12}. Members of P(A') are subsets of A'. The number of members containing exactly 3 elements is the number of ways to choose 3 elements from 6, namely C(6,3) = 6!/(3!3!) = 20. Thus option C 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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