If A = {1, 2, 3, 4}, how many subsets have an even sum?
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Answer and explanation
Correct answer: 8
The set has two odd elements, 1 and 3, and two even elements, 2 and 4. A subset has an even sum when it contains either zero or two odd elements. The number of choices is (choose 0 of 2 odd elements)(2^2 choices for even elements) plus (choose 2 of 2 odd elements)(2^2 choices for even elements), giving 4 + 4 = 8.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The set has two odd elements, 1 and 3, and two even elements, 2 and 4. A subset has an even sum when it contains either zero or two odd elements. The number of choices is (choose 0 of 2 odd elements)(2^2 choices for even elements) plus (choose 2 of 2 odd elements)(2^2 choices for even elements), giving 4 + 4 = 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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