If A = {1, 2, 3, 4, 5}, how many elements of P(A) contain 1, do not contain 2, and have exactly 3 elements?
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Answer and explanation
Correct answer: 3
We need three-element subsets of A that must include 1 and must exclude 2. Since 1 is already included, one additional element must be chosen from the remaining available elements {3, 4, 5}. There are C(3,1) = 3 choices, producing {1,3,4}, {1,3,5}, and {1,4,5}. Therefore, the answer is 3, which is option B.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
We need three-element subsets of A that must include 1 and must exclude 2. Since 1 is already included, one additional element must be chosen from the remaining available elements {3, 4, 5}. There are C(3,1) = 3 choices, producing {1,3,4}, {1,3,5}, and {1,4,5}. Therefore, the answer is 3, which is option B.
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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