If A = {1,2,3,4}, how many elements of P(A) have an even sum of elements?
Answer and explanation
Correct answer: 8
Only the odd elements 1 and 3 affect whether a subset sum is odd or even; the even elements 2 and 4 do not change parity. The sum is even when the subset contains an even number of odd elements: either neither 1 nor 3, or both 1 and 3. That gives 2 choices for the odd elements. The even elements are independently optional, giving 2² choices. Thus the total is 2 × 4 = 8, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
Only the odd elements 1 and 3 affect whether a subset sum is odd or even; the even elements 2 and 4 do not change parity. The sum is even when the subset contains an even number of odd elements: either neither 1 nor 3, or both 1 and 3. That gives 2 choices for the odd elements. The even elements are independently optional, giving 2² choices. Thus the total is 2 × 4 = 8, so option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
