If A = {1, 2} and B = {2, 3}, how many elements are in P(A) ∪ P(B)?
Answer and explanation
Correct answer: 6
First find the power sets: P(A) = {∅, {1}, {2}, {1,2}} and P(B) = {∅, {2}, {3}, {2,3}}. Each power set has 4 elements. Their common elements are ∅ and {2}, so the intersection has 2 elements. Using the union formula, n(P(A) ∪ P(B)) = 4 + 4 − 2 = 6. Therefore, option B is correct. It is important to compare the subsets themselves, not merely the original elements of A and B, when removing duplicates.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
First find the power sets: P(A) = {∅, {1}, {2}, {1,2}} and P(B) = {∅, {2}, {3}, {2,3}}. Each power set has 4 elements. Their common elements are ∅ and {2}, so the intersection has 2 elements. Using the union formula, n(P(A) ∪ P(B)) = 4 + 4 − 2 = 6. Therefore, option B is correct. It is important to compare the subsets themselves, not merely the original elements of A and B, when removing duplicates.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
