If A = {1, 2, 3}, how many two-element subsets does 𝒫(A) contain?
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Answer and explanation
Correct answer: 3
The elements of 𝒫(A) are the subsets of A. A two-element subset is formed by choosing any two of the three elements, without considering order. The number is therefore C(3, 2) = 3. These subsets are {1, 2}, {1, 3}, and {2, 3}. Thus 𝒫(A) contains three two-element subsets, so option C is correct.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
The elements of 𝒫(A) are the subsets of A. A two-element subset is formed by choosing any two of the three elements, without considering order. The number is therefore C(3, 2) = 3. These subsets are {1, 2}, {1, 3}, and {2, 3}. Thus 𝒫(A) contains three two-element subsets, so option C 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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