If A = {1, 3, 5, 7}, how many subsets have an odd sum?
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Answer and explanation
Correct answer: 8
Every element of A is odd. The sum of a subset is odd exactly when the subset contains an odd number of elements. Therefore, select either one element or three elements: C(4,1) + C(4,3) = 4 + 4 = 8. The empty set and all two-element or four-element subsets have even sums, so they are not counted.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
Every element of A is odd. The sum of a subset is odd exactly when the subset contains an odd number of elements. Therefore, select either one element or three elements: C(4,1) + C(4,3) = 4 + 4 = 8. The empty set and all two-element or four-element subsets have even sums, so they are not counted.
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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