If U = {1, 2, ..., 20}, A = {x ∈ U : 2 divides x}, and B = {x ∈ U : 5 divides x}, what is (A ∪ B)'?
Answer and explanation
Correct answer: {1, 3, 7, 9, 11, 13, 17, 19}
A contains the multiples of 2 in U, and B contains the multiples of 5. Thus A ∪ B contains every number divisible by 2 or by 5: {2, 4, 5, 6, 8, 10, 12, 14, 15, 16, 18, 20}. The complement contains the elements of U divisible by neither 2 nor 5, namely {1, 3, 7, 9, 11, 13, 17, 19}.
Frequently asked questions
What is the correct answer to this question?
{1, 3, 7, 9, 11, 13, 17, 19}
Why is this the correct answer?
A contains the multiples of 2 in U, and B contains the multiples of 5. Thus A ∪ B contains every number divisible by 2 or by 5: {2, 4, 5, 6, 8, 10, 12, 14, 15, 16, 18, 20}. The complement contains the elements of U divisible by neither 2 nor 5, namely {1, 3, 7, 9, 11, 13, 17, 19}.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
