If U = {1,2,3,4,5,6}, A = {1,2,3}, and B = {3,4,5}, what is n(P(A′ ∪ B′))?
Answer and explanation
Correct answer: 32
Using De Morgan’s law, A′ ∪ B′ = (A ∩ B)′. The intersection A ∩ B is {3}, so its complement in U is {1,2,4,5,6}, which has five elements. The power set of a five-element set contains 2⁵ = 32 elements. Therefore n(P(A′ ∪ B′)) = 32. Directly, A′ = {4,5,6} and B′ = {1,2,6}; their union is also {1,2,4,5,6}, confirming the result.
Frequently asked questions
What is the correct answer to this question?
32
Why is this the correct answer?
Using De Morgan’s law, A′ ∪ B′ = (A ∩ B)′. The intersection A ∩ B is {3}, so its complement in U is {1,2,4,5,6}, which has five elements. The power set of a five-element set contains 2⁵ = 32 elements. Therefore n(P(A′ ∪ B′)) = 32. Directly, A′ = {4,5,6} and B′ = {1,2,6}; their union is also {1,2,4,5,6}, confirming the result.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
