If U = {1,2,...,20}, A is the set of even numbers in U, and B is the set of multiples of 5 in U, which set does Aᶜ ∩ Bᶜ represent?
Answer and explanation
Correct answer: {1,3,7,9,11,13,17,19}, the numbers that are neither even nor multiples of 5
Aᶜ consists of numbers that are not even, and Bᶜ consists of numbers that are not multiples of 5. Their intersection therefore contains numbers satisfying both negative conditions: neither even nor a multiple of 5. In U these are {1,3,7,9,11,13,17,19}. This also follows from De Morgan’s law, Aᶜ ∩ Bᶜ = (A ∪ B)ᶜ, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
{1,3,7,9,11,13,17,19}, the numbers that are neither even nor multiples of 5
Why is this the correct answer?
Aᶜ consists of numbers that are not even, and Bᶜ consists of numbers that are not multiples of 5. Their intersection therefore contains numbers satisfying both negative conditions: neither even nor a multiple of 5. In U these are {1,3,7,9,11,13,17,19}. This also follows from De Morgan’s law, Aᶜ ∩ Bᶜ = (A ∪ B)ᶜ, 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.
