If U={1,2,3,4,5,6,7}, A={1,3,5,7}, how many elements does the power set P(A') of the complement of A with respect to U contain?
Answer and explanation
Correct answer: 8
First find the complement of A in U. The elements of U not in A are A'={2,4,6}, so |A'|=3. The power set of any finite set with n elements has 2^n elements, because every element has two independent choices: included or excluded. Hence |P(A')|=2^3=8. The value 16 would be the size of P(A), not P(A'), so option B is the only correct answer.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
First find the complement of A in U. The elements of U not in A are A'={2,4,6}, so |A'|=3. The power set of any finite set with n elements has 2^n elements, because every element has two independent choices: included or excluded. Hence |P(A')|=2^3=8. The value 16 would be the size of P(A), not P(A'), so option B is the only correct answer.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
