Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A = {x ∈ U : x is divisible by neither 2 nor 5}. What is A′, the complement of A in U?
Answer and explanation
Correct answer: {2, 4, 5, 6, 8, 10}
The governing idea is that the complement reverses the stated condition within U. Numbers in U divisible by neither 2 nor 5 are 1, 3, 7, and 9, so A = {1, 3, 7, 9}. Consequently A′ contains every element divisible by 2 or by 5: the even numbers 2, 4, 6, 8, 10 together with 5. Thus A′ = {2, 4, 5, 6, 8, 10}, making option A correct; option C wrongly omits multiples of 2 other than 10.
Frequently asked questions
What is the correct answer to this question?
{2, 4, 5, 6, 8, 10}
Why is this the correct answer?
The governing idea is that the complement reverses the stated condition within U. Numbers in U divisible by neither 2 nor 5 are 1, 3, 7, and 9, so A = {1, 3, 7, 9}. Consequently A′ contains every element divisible by 2 or by 5: the even numbers 2, 4, 6, 8, 10 together with 5. Thus A′ = {2, 4, 5, 6, 8, 10}, making option A correct; option C wrongly omits multiples of 2 other than 10.
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.
