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Class 10MathematicsSetsComplement of a Set and Its PropertiesMediumLevel 19

Let U={x∈N: 1≤x≤18}, A={x: x is divisible by 3}, and B={x: x is even}. How many elements are in Aᶜ∩Bᶜ?

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Answer and explanation

Correct answer: 6

Aᶜ∩Bᶜ contains numbers from 1 through 18 that are neither divisible by 3 nor even. The odd numbers in this range are 1,3,5,7,9,11,13,15,17. Removing the odd multiples of 3, namely 3,9, and 15, leaves {1,5,7,11,13,17}. Thus the set has 6 elements. Equivalently, De Morgan’s law gives Aᶜ∩Bᶜ=(A∪B)ᶜ.

Tags

setscomplementcountingDe Morgan lawsfinite universal setComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

6

Why is this the correct answer?

Aᶜ∩Bᶜ contains numbers from 1 through 18 that are neither divisible by 3 nor even. The odd numbers in this range are 1,3,5,7,9,11,13,15,17. Removing the odd multiples of 3, namely 3,9, and 15, leaves {1,5,7,11,13,17}. Thus the set has 6 elements. Equivalently, De Morgan’s law gives Aᶜ∩Bᶜ=(A∪B)ᶜ.

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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