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Class 10MathematicsSetsPower Set and SubsetsMediumLevel 15

If n(A) = 64, n(B) = 53, and n(A ∩ B) = 22, what is n(A' ∩ B)?

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Answer and explanation

Correct answer: 31

The set A' ∩ B consists of elements that are in B but not in A. Set B is partitioned into two disjoint parts: A ∩ B and A' ∩ B. Therefore n(B) = n(A ∩ B) + n(A' ∩ B). Substituting the given values gives 53 = 22 + n(A' ∩ B), so n(A' ∩ B) = 53 − 22 = 31. Thus option A is correct.

Tags

setscomplementintersectionset-differencecardinalityPower Set and SubsetsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

31

Why is this the correct answer?

The set A' ∩ B consists of elements that are in B but not in A. Set B is partitioned into two disjoint parts: A ∩ B and A' ∩ B. Therefore n(B) = n(A ∩ B) + n(A' ∩ B). Substituting the given values gives 53 = 22 + n(A' ∩ B), so n(A' ∩ B) = 53 − 22 = 31. Thus option A 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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