If U = {1,2,...,30}, A = {x : x is a multiple of 2}, and B = {x : x is a multiple of 3}, what is the smallest element of (A ∪ B)'?
Answer and explanation
Correct answer: 1
The complement (A ∪ B)' consists of elements of U that are not in A and not in B. Thus, its elements are numbers from 1 to 30 that are divisible by neither 2 nor 3. The number 1 is not divisible by 2 or 3, so it belongs to the complement. Because 1 is the smallest element of U, it is automatically the smallest element of (A ∪ B)'. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
1
Why is this the correct answer?
The complement (A ∪ B)' consists of elements of U that are not in A and not in B. Thus, its elements are numbers from 1 to 30 that are divisible by neither 2 nor 3. The number 1 is not divisible by 2 or 3, so it belongs to the complement. Because 1 is the smallest element of U, it is automatically the smallest element of (A ∪ B)'. Therefore, 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.
