If A={1,2,3}, how many elements of P(A) must contain 1?
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Answer and explanation
Correct answer: 4
The power set P(A) contains every subset of A. If the element 1 must be included, then the remaining elements 2 and 3 can each be either included or excluded independently. Thus there are 2 choices for 2 and 2 choices for 3, giving 2×2=2^2=4 subsets: {1}, {1,2}, {1,3}, and {1,2,3}. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The power set P(A) contains every subset of A. If the element 1 must be included, then the remaining elements 2 and 3 can each be either included or excluded independently. Thus there are 2 choices for 2 and 2 choices for 3, giving 2×2=2^2=4 subsets: {1}, {1,2}, {1,3}, and {1,2,3}. Therefore, option A 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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