If A = {1, 2, 3, 4}, how many subsets in P(A) contain 1 and do not contain 4?
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Answer and explanation
Correct answer: 4
The conditions require 1 to be included and 4 to be excluded, so neither of these elements is free to vary. Only 2 and 3 remain, and each can independently be included or excluded. Thus the number of valid subsets is 2 × 2 = 2^2 = 4. They are {1}, {1, 2}, {1, 3}, and {1, 2, 3}; therefore, option B is correct.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The conditions require 1 to be included and 4 to be excluded, so neither of these elements is free to vary. Only 2 and 3 remain, and each can independently be included or excluded. Thus the number of valid subsets is 2 × 2 = 2^2 = 4. They are {1}, {1, 2}, {1, 3}, and {1, 2, 3}; 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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