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Class 10MathematicsSetsPower Set and SubsetsEasyLevel 10

If A = {3, 6, 9, 12}, how many non-empty subsets are there in P(A)?

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Answer and explanation

Correct answer: 15

The set A has 4 elements. A set with n elements has 2ⁿ subsets because each element can either be included or excluded. Therefore, P(A) has 2⁴ = 16 subsets in total. Exactly one of these subsets is the empty set, ∅. Hence, the number of non-empty subsets is 16 − 1 = 15, so option B is correct.

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setspower setnon-empty subsetsPower Set and SubsetsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

15

Why is this the correct answer?

The set A has 4 elements. A set with n elements has 2ⁿ subsets because each element can either be included or excluded. Therefore, P(A) has 2⁴ = 16 subsets in total. Exactly one of these subsets is the empty set, ∅. Hence, the number of non-empty subsets is 16 − 1 = 15, so option B 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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