If A = {1, 2} and B = {3, 4}, how many members are in P(A ∪ B) − (P(A) ∪ P(B))?
Answer and explanation
Correct answer: 9
Since A and B are disjoint and each has two elements, A ∪ B = {1, 2, 3, 4}, so |P(A ∪ B)| = 2^4 = 16. Also, |P(A)| = |P(B)| = 2^2 = 4. The two power sets share only the empty set, because no nonempty subset can consist simultaneously of elements from A and from B. Thus |P(A) ∪ P(B)| = 4 + 4 − 1 = 7, and the required difference has 16 − 7 = 9 members.
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
Since A and B are disjoint and each has two elements, A ∪ B = {1, 2, 3, 4}, so |P(A ∪ B)| = 2^4 = 16. Also, |P(A)| = |P(B)| = 2^2 = 4. The two power sets share only the empty set, because no nonempty subset can consist simultaneously of elements from A and from B. Thus |P(A) ∪ P(B)| = 4 + 4 − 1 = 7, and the required difference has 16 − 7 = 9 members.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
