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Class 10MathematicsSetsPower Set and SubsetsHardLevel 10

If U={1,2,3,4,5} and A={1,4}, what is P(A)∩P(A')?

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Answer and explanation

Correct answer: {∅}

Here A'={2,3,5}. A and A' are disjoint, so a set that is a subset of both can contain no element from A and no element from A'. The empty set is the only set with no elements, and it is a subset of every set. Thus P(A)∩P(A')={∅}, not ∅; option B is correct.

Tags

setscomplementpower-setintersectionPower Set and SubsetsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

{∅}

Why is this the correct answer?

Here A'={2,3,5}. A and A' are disjoint, so a set that is a subset of both can contain no element from A and no element from A'. The empty set is the only set with no elements, and it is a subset of every set. Thus P(A)∩P(A')={∅}, not ∅; 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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