If U = {2, 4, 6} and A = ∅, how many elements are in P(A′)?
Advertisement
Answer and explanation
Correct answer: 8
Since A is the empty set and the complement is taken relative to U, A′ = U − A = U = {2, 4, 6}. This set has three elements. The power set of an n-element set contains 2^n subsets, because each element can either be included or excluded. Hence |P(A′)| = 2^3 = 8, making option C correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
Since A is the empty set and the complement is taken relative to U, A′ = U − A = U = {2, 4, 6}. This set has three elements. The power set of an n-element set contains 2^n subsets, because each element can either be included or excluded. Hence |P(A′)| = 2^3 = 8, making option C correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
Advertisement