If A = {1, 2, 3, 4}, how many subsets in P(A) contain 2 and do not contain 3?
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Answer and explanation
Correct answer: 4
The condition requires 2 to be included and 3 to be excluded, so those two choices are fixed. Only 1 and 4 remain freely selectable. Each can be included or omitted independently, giving 2 × 2 = 2^2 = 4 valid subsets: {2}, {1,2}, {2,4}, and {1,2,4}. Therefore, option B is correct.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The condition requires 2 to be included and 3 to be excluded, so those two choices are fixed. Only 1 and 4 remain freely selectable. Each can be included or omitted independently, giving 2 × 2 = 2^2 = 4 valid subsets: {2}, {1,2}, {2,4}, and {1,2,4}. Therefore, 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.
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