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Class 12MathematicsSetsMediumLevel 7
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If A = {1, 2, 3}, how many subsets of A have at least two elements?

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Answer and explanation

Correct answer: 4

“At least two elements” means subsets with exactly two elements or exactly three elements. There are C(3,2) = 3 subsets with two elements: {1,2}, {1,3}, and {2,3}. There is C(3,3) = 1 subset with three elements, namely A itself. Thus the total is 3 + 1 = 4, so option B is correct.

Related tags

SetsSubset CountingCombinationsCardinalityMathematicsClass 12 Mcq

Frequently asked questions

What is the correct answer to this question?

4

Why is this the correct answer?

“At least two elements” means subsets with exactly two elements or exactly three elements. There are C(3,2) = 3 subsets with two elements: {1,2}, {1,3}, and {2,3}. There is C(3,3) = 1 subset with three elements, namely A itself. Thus the total is 3 + 1 = 4, so option B is correct.

Which subject and chapter does this question cover?

This is a Class 12 Mathematics question. Chapter: Sets.

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