If A = {1, 2, 3, 4, 5}, how many subsets of A have at most two elements?
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Answer and explanation
Correct answer: 16
The phrase “at most two elements” includes subsets containing 0, 1, or 2 elements. From a five-element set, there is C(5,0) = 1 empty subset, C(5,1) = 5 one-element subsets, and C(5,2) = 10 two-element subsets. Therefore, the required total is 1 + 5 + 10 = 16, so option C is correct.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
The phrase “at most two elements” includes subsets containing 0, 1, or 2 elements. From a five-element set, there is C(5,0) = 1 empty subset, C(5,1) = 5 one-element subsets, and C(5,2) = 10 two-element subsets. Therefore, the required total is 1 + 5 + 10 = 16, 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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