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Subjects
Class 10MathematicsSetsPower Set and SubsetsHardLevel 9

If A = {1,2,3,4,5}, how many members of P(A) have an even sum of elements?

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Answer and explanation

Correct answer: 16

There are 2^5 = 32 subsets in P(A). Pair every subset S with S △ {1}, where 1 is odd; toggling 1 changes the parity of the subset sum. Thus each pair contains one even-sum subset and one odd-sum subset. Consequently the 32 subsets divide equally, and the number with an even sum is 32/2 = 16.

Tags

setspower-setparitysubset-sumPower Set and SubsetsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

16

Why is this the correct answer?

There are 2^5 = 32 subsets in P(A). Pair every subset S with S △ {1}, where 1 is odd; toggling 1 changes the parity of the subset sum. Thus each pair contains one even-sum subset and one odd-sum subset. Consequently the 32 subsets divide equally, and the number with an even sum is 32/2 = 16.

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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