If n(𝒫(A)) = 32, how many proper subsets does A have?
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Answer and explanation
Correct answer: 31
If a finite set A has n elements, then its power set 𝒫(A) has 2ⁿ elements. Here, 2ⁿ = 32 = 2⁵, so A has 5 elements. Therefore, A has 32 subsets in total. A proper subset is any subset other than A itself, so we exclude exactly one subset: A. Hence, the number of proper subsets is 32 − 1 = 31.
Frequently asked questions
What is the correct answer to this question?
31
Why is this the correct answer?
If a finite set A has n elements, then its power set 𝒫(A) has 2ⁿ elements. Here, 2ⁿ = 32 = 2⁵, so A has 5 elements. Therefore, A has 32 subsets in total. A proper subset is any subset other than A itself, so we exclude exactly one subset: A. Hence, the number of proper subsets is 32 − 1 = 31.
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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