If A = {1, 2, 3, 4}, how many subsets have an even sum of elements?
Answer and explanation
Correct answer: 8
The elements 1 and 3 are odd, while 2 and 4 are even. A subset has an even total when it contains either zero or two odd elements. Among the 16 subsets of A, exactly half have an even sum and half have an odd sum. Therefore, the number of subsets with even sum is 16 ÷ 2 = 8. The empty subset is included because its sum is 0, which is even.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The elements 1 and 3 are odd, while 2 and 4 are even. A subset has an even total when it contains either zero or two odd elements. Among the 16 subsets of A, exactly half have an even sum and half have an odd sum. Therefore, the number of subsets with even sum is 16 ÷ 2 = 8. The empty subset is included because its sum is 0, which is even.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
