If U = {1, 2, ..., 45}, A = {x : x is a multiple of 3}, and B = {x : x is a multiple of 5}, what is the greatest element of (A ∪ B)'?
Answer and explanation
Correct answer: 44
The complement of A ∪ B contains the elements of U that are divisible by neither 3 nor 5. The largest element of U is 45, but it is divisible by both 3 and 5. The next number, 44, is not divisible by 3 and is not divisible by 5. Therefore 44 belongs to the complement and is its greatest element. Option A is correct.
Frequently asked questions
What is the correct answer to this question?
44
Why is this the correct answer?
The complement of A ∪ B contains the elements of U that are divisible by neither 3 nor 5. The largest element of U is 45, but it is divisible by both 3 and 5. The next number, 44, is not divisible by 3 and is not divisible by 5. Therefore 44 belongs to the complement and is its greatest element. Option A 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.
