What is the roster form of S = {x : x is a positive integer less than 15 and x is coprime to 15}?
Answer and explanation
Correct answer: S = {1, 2, 4, 7, 8, 11, 13, 14}
The positive integers less than 15 are 1 through 14. Since 15 = 3 × 5, a number is coprime to 15 precisely when it is divisible by neither 3 nor 5. Testing the integers gives 1, 2, 4, 7, 8, 11, 13, and 14. Their greatest common divisor with 15 is 1, while every omitted number shares a factor with 15. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
S = {1, 2, 4, 7, 8, 11, 13, 14}
Why is this the correct answer?
The positive integers less than 15 are 1 through 14. Since 15 = 3 × 5, a number is coprime to 15 precisely when it is divisible by neither 3 nor 5. Testing the integers gives 1, 2, 4, 7, 8, 11, 13, and 14. Their greatest common divisor with 15 is 1, while every omitted number shares a factor with 15. Hence option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
