If U = {1,2,3,4,5,6,7,8,9,10} and A = {2,3,5,7}, what is |𝒫(A′)|?
Answer and explanation
Correct answer: 64
The set A contains four elements. Its complement relative to the given universal set U therefore contains 10 − 4 = 6 elements; explicitly, A′ = {1,4,6,8,9,10}. Every element may either be included or excluded from a subset, so a six-element set has 2^6 = 64 subsets. Consequently, |𝒫(A′)| = 64, and option C is the only correct answer.
Frequently asked questions
What is the correct answer to this question?
64
Why is this the correct answer?
The set A contains four elements. Its complement relative to the given universal set U therefore contains 10 − 4 = 6 elements; explicitly, A′ = {1,4,6,8,9,10}. Every element may either be included or excluded from a subset, so a six-element set has 2^6 = 64 subsets. Consequently, |𝒫(A′)| = 64, and option C is the only correct answer.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
