If A ∩ B = ∅, |A| = 4, and |B| = 3, what is |P(A) ∪ P(B)|?
Advertisement
Answer and explanation
Correct answer: 23
Since A and B are disjoint, their only common subset is the empty set ∅. The power set of a set with n elements has 2ⁿ members, so |P(A)| = 2⁴ = 16 and |P(B)| = 2³ = 8. When taking the union, ∅ is counted twice and must be subtracted once. Therefore, |P(A) ∪ P(B)| = 16 + 8 − 1 = 23.
Frequently asked questions
What is the correct answer to this question?
23
Why is this the correct answer?
Since A and B are disjoint, their only common subset is the empty set ∅. The power set of a set with n elements has 2ⁿ members, so |P(A)| = 2⁴ = 16 and |P(B)| = 2³ = 8. When taking the union, ∅ is counted twice and must be subtracted once. Therefore, |P(A) ∪ P(B)| = 16 + 8 − 1 = 23.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
Advertisement