The universal set is U = {x : x ∈ N, 1 ≤ x ≤ 10} and A = {2,4,6,8,10}. How many singleton sets are in P(A')?
Answer and explanation
Correct answer: 5
The universal set contains the integers from 1 through 10. Removing the elements of A leaves A' = {1,3,5,7,9}, which has five elements. A singleton subset of A' contains exactly one element, so there is one singleton subset for each element of A': {1}, {3}, {5}, {7}, and {9}. Hence P(A') contains exactly five singleton sets, making option B correct. The total size of P(A') is 32, but that is not the number of singleton members.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
The universal set contains the integers from 1 through 10. Removing the elements of A leaves A' = {1,3,5,7,9}, which has five elements. A singleton subset of A' contains exactly one element, so there is one singleton subset for each element of A': {1}, {3}, {5}, {7}, and {9}. Hence P(A') contains exactly five singleton sets, making option B correct. The total size of P(A') is 32, but that is not the number of singleton members.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
