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Class 12MathematicsSetsMediumLevel 7
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If A = {1, 2, 3, 4}, how many proper subsets of A have exactly three elements?

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Answer and explanation

Correct answer: 4

A three-element subset of A is obtained by choosing 3 elements from the 4 available elements. The number of choices is C(4, 3) = 4. Each such subset omits exactly one element, so none is equal to A; hence every one is a proper subset. The four subsets are {1,2,3}, {1,2,4}, {1,3,4}, and {2,3,4}.

Related tags

SetsProper SubsetsCombinationsPower SetMathematicsClass 12 Mcq

Frequently asked questions

What is the correct answer to this question?

4

Why is this the correct answer?

A three-element subset of A is obtained by choosing 3 elements from the 4 available elements. The number of choices is C(4, 3) = 4. Each such subset omits exactly one element, so none is equal to A; hence every one is a proper subset. The four subsets are {1,2,3}, {1,2,4}, {1,3,4}, and {2,3,4}.

Which subject and chapter does this question cover?

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

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