If A = {x ∈ Z : −2 ≤ x ≤ 3}, what is |P(A)|?
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Answer and explanation
Correct answer: 64
Because the endpoints are included, the integers in A are −2, −1, 0, 1, 2, and 3. Thus A contains 6 elements. For every finite set with n elements, the number of subsets in its power set is 2^n, because each element can either be selected or not selected. Therefore |P(A)| = 2^6 = 64. Hence option C is correct.
Frequently asked questions
What is the correct answer to this question?
64
Why is this the correct answer?
Because the endpoints are included, the integers in A are −2, −1, 0, 1, 2, and 3. Thus A contains 6 elements. For every finite set with n elements, the number of subsets in its power set is 2^n, because each element can either be selected or not selected. Therefore |P(A)| = 2^6 = 64. Hence option C is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
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