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Class 10MathematicsSetsComplement of a Set and Its PropertiesMediumLevel 19

If U = {1, 2, ..., 20}, A = {x : x ∈ U and x is even}, and B = {x : x ∈ U and x is prime}, what is A′ ∩ B?

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Answer and explanation

Correct answer: {3, 5, 7, 11, 13, 17, 19}

A contains all even numbers in U, so A′ contains all odd numbers from 1 to 20. The prime numbers in U are 2, 3, 5, 7, 11, 13, 17, and 19. Intersecting this prime set with A′ removes 2 because it is even. The remaining odd primes are {3, 5, 7, 11, 13, 17, 19}, which is therefore A′ ∩ B.

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setscomplementintersectionprime-numbersComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

{3, 5, 7, 11, 13, 17, 19}

Why is this the correct answer?

A contains all even numbers in U, so A′ contains all odd numbers from 1 to 20. The prime numbers in U are 2, 3, 5, 7, 11, 13, 17, and 19. Intersecting this prime set with A′ removes 2 because it is even. The remaining odd primes are {3, 5, 7, 11, 13, 17, 19}, which is therefore A′ ∩ B.

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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