If A = {2, 4, 6, 8, 10}, how many elements does 𝒫(A) have?
Answer and explanation
Correct answer: 32
The set A contains five distinct elements: 2, 4, 6, 8, and 10. For every element, a subset can either include it or exclude it, giving two choices independently. Therefore, a set with n elements has 2ⁿ subsets. Here n = 5, so |𝒫(A)| = 2⁵ = 32. The requested number is the cardinality of the power set, not the number of elements in A.
Frequently asked questions
What is the correct answer to this question?
32
Why is this the correct answer?
The set A contains five distinct elements: 2, 4, 6, 8, and 10. For every element, a subset can either include it or exclude it, giving two choices independently. Therefore, a set with n elements has 2ⁿ subsets. Here n = 5, so |𝒫(A)| = 2⁵ = 32. The requested number is the cardinality of the power set, not the number of elements in A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
