If n(A) = 5, how many elements does P(A) contain?
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Answer and explanation
Correct answer: 32
A set with n elements has exactly 2^n subsets, because each element can either be included or excluded independently. Since n(A) = 5, the number of elements in the power set is n(P(A)) = 2^5 = 32. Thus, P(A) contains 32 subsets, including the empty set and the original set A itself.
Frequently asked questions
What is the correct answer to this question?
32
Why is this the correct answer?
A set with n elements has exactly 2^n subsets, because each element can either be included or excluded independently. Since n(A) = 5, the number of elements in the power set is n(P(A)) = 2^5 = 32. Thus, P(A) contains 32 subsets, including the empty set and the original set A itself.
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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