Let U = {1, 2, 3, 4, 5, 6, 7, 8}, A = {1, 3, 5, 7}, and B = {2, 3, 5, 8}. What is |P((A ∪ B)')|, where the complement is taken relative to U?
Answer and explanation
Correct answer: 4
First form the union: A ∪ B = {1, 2, 3, 5, 7, 8}. Taking the complement relative to the universal set U leaves the elements of U that are not in this union: (A ∪ B)' = {4, 6}. This complement has 2 elements. A set with n elements has 2^n subsets, so the power set P((A ∪ B)') has 2^2 = 4 members. Therefore, option B is correct. The order matters: find the union first, then take its complement in U, and finally count the power set.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
First form the union: A ∪ B = {1, 2, 3, 5, 7, 8}. Taking the complement relative to the universal set U leaves the elements of U that are not in this union: (A ∪ B)' = {4, 6}. This complement has 2 elements. A set with n elements has 2^n subsets, so the power set P((A ∪ B)') has 2^2 = 4 members. Therefore, option B is correct. The order matters: find the union first, then take its complement in U, and finally count the power set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
