Find the number of distinct rational numbers `x` such that `o < x < 1a n dx=p//q` , where `p ,q in {1,2,3,4,5,6}` .

Options

A. 15
B. 13
C. 12
D. 11

Explanation

To find the number of distinct rational numbers \( x \) such that \( 0 < x < 1 \) and \( x = \frac{p}{q} \) where \( p, q \in \{1, 2, 3, 4, 5, 6\} \), we can follow these steps:

### Step 1: Identify the possible values for \( p \) and \( q \)
We have the set \( \{1, 2, 3, 4, 5, 6\} \). Here, \( p \) must be less than \( q \) to ensure that \( x \) is between 0 and 1.

### Step 2: Count the total combinations of \( p \) and \( q \)
We need to choose 2 numbers from the set of 6 numbers. The number of ways to choose 2 numbers from 6 is given by the combination formula:

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