If U = {1,2,3,4,5,6,7} and A = {2,4,6}, how many members of P(U) are subsets of A′?
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Answer and explanation
Correct answer: 16
The complement of A relative to U is A′ = U − A = {1,3,5,7}. It has 4 elements. A member of P(U) that is a subset of A′ can be any subset of A′, including the empty set and A′ itself. Therefore, the number of such members equals |P(A′)| = 2⁴ = 16. Thus option B is correct.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
The complement of A relative to U is A′ = U − A = {1,3,5,7}. It has 4 elements. A member of P(U) that is a subset of A′ can be any subset of A′, including the empty set and A′ itself. Therefore, the number of such members equals |P(A′)| = 2⁴ = 16. Thus 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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