Let U = {1, 2, 3, 4, 5, 6} be the universal set and A = {1, 2, 3}. What is P(A′) ∩ P(A), where A′ is the complement of A in U?
Answer and explanation
Correct answer: {∅}
The complement of A in U is A′ = {4, 5, 6}. Since A = {1, 2, 3} and A′ = {4, 5, 6} have no common element, the only subset common to both sets is the empty set ∅. Therefore, the only common member of their power sets is ∅ itself, so P(A′) ∩ P(A) = {∅}. It is {∅}, not ∅, because the power set contains the empty set as an element.
Frequently asked questions
What is the correct answer to this question?
{∅}
Why is this the correct answer?
The complement of A in U is A′ = {4, 5, 6}. Since A = {1, 2, 3} and A′ = {4, 5, 6} have no common element, the only subset common to both sets is the empty set ∅. Therefore, the only common member of their power sets is ∅ itself, so P(A′) ∩ P(A) = {∅}. It is {∅}, not ∅, because the power set contains the empty set as an element.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
