If A={1,2,3,4}, how many subsets in P(A) contain 1 but do not contain 4?
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Answer and explanation
Correct answer: 4
The condition fixes two elements: 1 must be included and 4 must be excluded. The remaining elements 2 and 3 are unrestricted, so each can independently be selected or not selected. Hence the number of valid subsets is 2^2=4. Explicitly, they are {1}, {1,2}, {1,3}, and {1,2,3}. Thus option A is the only correct answer.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The condition fixes two elements: 1 must be included and 4 must be excluded. The remaining elements 2 and 3 are unrestricted, so each can independently be selected or not selected. Hence the number of valid subsets is 2^2=4. Explicitly, they are {1}, {1,2}, {1,3}, and {1,2,3}. Thus option A is the only correct answer.
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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