Let F be the set of fractions in simplest form between 0 and 1 that can be written with a single-digit denominator. Find F and |F|​

|F| is 27, the whole F is "listed" below.

Step-by-step explanation:

The set of possible denominators is the numbers from 2 to 9. Each of them produces a single fraction for each numerator that's coprime to it.

Let's list those for each:

2: 1

3: 1 2

4: 1 3 (2 is not coprime)

5: 1 2 3 4

6: 1 5 (2 3 and 4 are not coprime)

7: 1 2 3 4 5 6

8: 1 3 5 7

9: 1 2 4 5 7 8 (3 and 6 are not coprime)

To make any number from F, just take the denominator from the rows and the numerator from the list. The size of F is 1 + 2 + 2 + 4 + 2 + 6 + 4 + 6 = 27