If U={1,2,3,...,18} and A={x:x is divisible by both 2 and 5}, what is A^c?
Answer and explanation
Correct answer: {1,2,3,4,5,6,7,8,9,11,12,13,14,15,16,17,18}
A number divisible by both 2 and 5 must be divisible by their least common multiple, 10. Between 1 and 18, the only multiple of 10 is 10, so A={10}. The complement contains every element of U except 10. Hence A^c={1,2,3,4,5,6,7,8,9,11,12,13,14,15,16,17,18}, which is option A.
Frequently asked questions
What is the correct answer to this question?
{1,2,3,4,5,6,7,8,9,11,12,13,14,15,16,17,18}
Why is this the correct answer?
A number divisible by both 2 and 5 must be divisible by their least common multiple, 10. Between 1 and 18, the only multiple of 10 is 10, so A={10}. The complement contains every element of U except 10. Hence A^c={1,2,3,4,5,6,7,8,9,11,12,13,14,15,16,17,18}, which is option A.
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.
