If U = {1,2,3,4,5}, A = {1,2}, and B = {2,3,4}, what is n(P((A ∩ B)′))?
Answer and explanation
Correct answer: 16
First find the intersection: A ∩ B = {2}. The complement is taken relative to the stated universal set U, so (A ∩ B)′ = U − {2} = {1,3,4,5}. This complement has four elements. The power set of a four-element set has 2⁴ = 16 elements. Therefore n(P((A ∩ B)′)) = 16. The value 4 is only the size of the complement, not the size of its power set.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
First find the intersection: A ∩ B = {2}. The complement is taken relative to the stated universal set U, so (A ∩ B)′ = U − {2} = {1,3,4,5}. This complement has four elements. The power set of a four-element set has 2⁴ = 16 elements. Therefore n(P((A ∩ B)′)) = 16. The value 4 is only the size of the complement, not the size of its power set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
