If U = {1,2,3,4,5,6,7,8} and A = {1,3,5,7}, how many elements of P(A′) contain only even numbers?
Answer and explanation
Correct answer: 16
The complement of A with respect to U is A′ = U − A = {2,4,6,8}. It has four elements, and every one of them is even. A set with n elements has 2ⁿ subsets, so P(A′) contains 2⁴ = 16 subsets. Since A′ itself contains only even numbers, every subset of A′ also contains only even numbers, including the empty set. Therefore, the correct answer is 16.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
The complement of A with respect to U is A′ = U − A = {2,4,6,8}. It has four elements, and every one of them is even. A set with n elements has 2ⁿ subsets, so P(A′) contains 2⁴ = 16 subsets. Since A′ itself contains only even numbers, every subset of A′ also contains only even numbers, including the empty set. Therefore, the correct answer is 16.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
