If A = {1, 2, 3}, how many sets in P(A) contain 1?
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Answer and explanation
Correct answer: 4
To form a subset of A that contains 1, keep 1 fixed. The other two elements, 2 and 3, may each be either included or excluded independently. Therefore there are 2 choices for 2 and 2 choices for 3, giving 2 × 2 = 2^2 = 4 subsets. They are {1}, {1,2}, {1,3}, and {1,2,3}.
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 contains 1, keep 1 fixed. The other two elements, 2 and 3, may each be either included or excluded independently. Therefore there are 2 choices for 2 and 2 choices for 3, giving 2 × 2 = 2^2 = 4 subsets. They are {1}, {1,2}, {1,3}, and {1,2,3}.
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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