If U = {1, 2, 3, 4, 5, 6} and A = {2, 4, 6}, which of the following is not a member of P(A′)?
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Answer and explanation
Correct answer: {2}
The complement of A with respect to U is A′ = U − A = {1, 3, 5}. The power set P(A′) contains every subset of {1, 3, 5}, including ∅, {1, 3}, and {5}. However, {2} contains the element 2, which is not in A′, so {2} is not a subset of A′ and therefore is not a member of P(A′). Hence, option D is correct.
Frequently asked questions
What is the correct answer to this question?
{2}
Why is this the correct answer?
The complement of A with respect to U is A′ = U − A = {1, 3, 5}. The power set P(A′) contains every subset of {1, 3, 5}, including ∅, {1, 3}, and {5}. However, {2} contains the element 2, which is not in A′, so {2} is not a subset of A′ and therefore is not a member of P(A′). Hence, option D 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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