If A = {1, 2, 3, 4}, how many two-element subsets will be in P(A)?
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Answer and explanation
Correct answer: 6
A two-element subset is formed by choosing any 2 different elements from the 4 elements of A. The number of such choices is C(4,2) = 4!/(2!2!) = (4 × 3)/(2 × 1) = 6. These subsets are {1,2}, {1,3}, {1,4}, {2,3}, {2,4}, and {3,4}. Therefore P(A) contains 6 two-element subsets, making option B correct.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
A two-element subset is formed by choosing any 2 different elements from the 4 elements of A. The number of such choices is C(4,2) = 4!/(2!2!) = (4 × 3)/(2 × 1) = 6. These subsets are {1,2}, {1,3}, {1,4}, {2,3}, {2,4}, and {3,4}. Therefore P(A) contains 6 two-element subsets, making option B 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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