If A = {2, 4, 6, 8, 10}, how many sets in P(A) have exactly 2 elements?
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Answer and explanation
Correct answer: 10
The power set contains all subsets of A. To form a subset with exactly 2 elements, choose any 2 of the 5 elements, without considering order. The number of choices is the combination 5C2 = 5!/(2!3!) = (5 × 4)/2 = 10. Therefore P(A) contains exactly 10 two-element subsets, making option B correct.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
The power set contains all subsets of A. To form a subset with exactly 2 elements, choose any 2 of the 5 elements, without considering order. The number of choices is the combination 5C2 = 5!/(2!3!) = (5 × 4)/2 = 10. Therefore P(A) contains exactly 10 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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