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Class 10MathematicsSetsComplement of a Set and Its PropertiesMediumLevel 10

If U = {p,q,r,s,t}, A = {p,q,r}, and B = {r,s}, what is (A ∩ B)′?

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Answer and explanation

Correct answer: {p,q,s,t}

First find the intersection. The only element common to A = {p,q,r} and B = {r,s} is r, so A ∩ B = {r}. The complement is taken in U, not in an unrestricted universe. Removing r from U = {p,q,r,s,t} leaves {p,q,s,t}. Hence (A ∩ B)′ = {p,q,s,t}, so option B is correct.

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setsintersectioncomplementComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

{p,q,s,t}

Why is this the correct answer?

First find the intersection. The only element common to A = {p,q,r} and B = {r,s} is r, so A ∩ B = {r}. The complement is taken in U, not in an unrestricted universe. Removing r from U = {p,q,r,s,t} leaves {p,q,s,t}. Hence (A ∩ B)′ = {p,q,s,t}, so option B is correct.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.

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