If A={a,b,c,d}, how many elements of P(A) are subsets with an odd number of elements?
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Answer and explanation
Correct answer: 8
A has 4 elements. The odd-cardinality subsets must contain either 1 element or 3 elements. Their number is C(4,1)+C(4,3)=4+4=8. Equivalently, for every nonempty finite set, exactly half of its 2^n subsets have odd cardinality and half have even cardinality. Since |P(A)|=16, the number of odd-sized subsets is 16/2=8.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
A has 4 elements. The odd-cardinality subsets must contain either 1 element or 3 elements. Their number is C(4,1)+C(4,3)=4+4=8. Equivalently, for every nonempty finite set, exactly half of its 2^n subsets have odd cardinality and half have even cardinality. Since |P(A)|=16, the number of odd-sized subsets is 16/2=8.
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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