If A = {1, 3, 5}, how many subsets in P(A) must contain 3?
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Answer and explanation
Correct answer: 4
To form a subset of A that must contain 3, include 3 first. The remaining elements, 1 and 5, can each be either included or excluded independently. Thus there are 2 choices for 1 and 2 choices for 5, giving 2 × 2 = 2² = 4 subsets. They are {3}, {1,3}, {3,5}, and {1,3,5}. Therefore, option B is correct.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
To form a subset of A that must contain 3, include 3 first. The remaining elements, 1 and 5, can each be either included or excluded independently. Thus there are 2 choices for 1 and 2 choices for 5, giving 2 × 2 = 2² = 4 subsets. They are {3}, {1,3}, {3,5}, and {1,3,5}. 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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