If A = {1, 2, 3, 4}, how many subsets either contain both 2 and 3 or contain neither of them?
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Answer and explanation
Correct answer: 8
Consider the pair 2 and 3. There are two allowed cases: both are included, or both are excluded. In either case, the remaining elements 1 and 4 can each be independently included or excluded, giving 2^2 = 4 choices. Thus the total number is 4 + 4 = 8, or equivalently 2 × 2^2 = 8. Hence option C is correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
Consider the pair 2 and 3. There are two allowed cases: both are included, or both are excluded. In either case, the remaining elements 1 and 4 can each be independently included or excluded, giving 2^2 = 4 choices. Thus the total number is 4 + 4 = 8, or equivalently 2 × 2^2 = 8. Hence option C is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
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