If U = {1,2,3,4,5,6,7,8}, A = {1,2,3,4}, and B = {3,4,5,6}, what is |P(A' ∩ B')|, where complements are taken with respect to U?
Advertisement
Answer and explanation
Correct answer: 4
Use De Morgan’s law or calculate directly. A ∪ B = {1,2,3,4,5,6}, so its complement in U is {7,8}; hence A' ∩ B' = {7,8}. This set has two elements, and the power-set rule gives |P(A' ∩ B')| = 2² = 4. Therefore option B is correct. The other values correspond to using an incorrect number of elements in the final set.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
Use De Morgan’s law or calculate directly. A ∪ B = {1,2,3,4,5,6}, so its complement in U is {7,8}; hence A' ∩ B' = {7,8}. This set has two elements, and the power-set rule gives |P(A' ∩ B')| = 2² = 4. Therefore option B is correct. The other values correspond to using an incorrect number of elements in the final set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
Advertisement