If A = {x : x ∈ ℤ, −2 ≤ x ≤ 2}, how many elements does the power set P(A) have?
Answer and explanation
Correct answer: 32
The integers from −2 through 2 are −2, −1, 0, 1, and 2, so A has 5 elements. A set with n elements has exactly 2ⁿ subsets because each element can independently be included or excluded. Therefore, |P(A)| = 2⁵ = 32. The answer is consequently option C, not 16 or 64, which would result from counting the elements of A incorrectly.
Frequently asked questions
What is the correct answer to this question?
32
Why is this the correct answer?
The integers from −2 through 2 are −2, −1, 0, 1, and 2, so A has 5 elements. A set with n elements has exactly 2ⁿ subsets because each element can independently be included or excluded. Therefore, |P(A)| = 2⁵ = 32. The answer is consequently option C, not 16 or 64, which would result from counting the elements of A incorrectly.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
