If A = {1, 2, 3, 4}, how many subsets of A contain exactly one odd number?
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Answer and explanation
Correct answer: 8
The odd elements of A are 1 and 3. Exactly one of these two must be selected, which can be done in C(2,1) = 2 ways. The even elements 2 and 4 have no restriction, so each may be included or excluded independently, giving 2² = 4 choices. Therefore the total number is C(2,1) × 2² = 2 × 4 = 8. Hence option D is correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The odd elements of A are 1 and 3. Exactly one of these two must be selected, which can be done in C(2,1) = 2 ways. The even elements 2 and 4 have no restriction, so each may be included or excluded independently, giving 2² = 4 choices. Therefore the total number is C(2,1) × 2² = 2 × 4 = 8. Hence option D is correct.
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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