If n(A)=m and n(P(A))=n(A)+12, what is m?
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Answer and explanation
Correct answer: 4
A finite set with m elements has 2^m elements in its power set. Therefore, the given condition becomes 2^m=m+12. Testing the options, m=4 gives 2^4=16 and m+12=4+12=16, so the equation is satisfied. The other listed values do not satisfy it; hence m=4.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
A finite set with m elements has 2^m elements in its power set. Therefore, the given condition becomes 2^m=m+12. Testing the options, m=4 gives 2^4=16 and m+12=4+12=16, so the equation is satisfied. The other listed values do not satisfy it; hence m=4.
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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