Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A = {x : x ∈ U and x is even}. How many elements of P(A′) have exactly two elements?
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Answer and explanation
Correct answer: 10
The even elements of U form A = {2, 4, 6, 8, 10}. Therefore its complement is A′ = {1, 3, 5, 7, 9}, which has 5 elements. The elements of P(A′) are all subsets of A′. A subset with exactly two elements can be selected in C(5, 2) ways = 5!/(2!3!) = 10. Hence P(A′) contains 10 two-element subsets, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
The even elements of U form A = {2, 4, 6, 8, 10}. Therefore its complement is A′ = {1, 3, 5, 7, 9}, which has 5 elements. The elements of P(A′) are all subsets of A′. A subset with exactly two elements can be selected in C(5, 2) ways = 5!/(2!3!) = 10. Hence P(A′) contains 10 two-element subsets, so 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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