State true of false
If x and y are two rational numbers such that x `gt` y, then x - y is always a positive rational number.

Answer

To determine whether the statement "If x and y are two rational numbers such that x > y, then x - y is always a positive rational number" is true or false, we can analyze it step by step.

### Step 1: Understanding Rational Numbers
A rational number is defined as a number that can be expressed in the form of \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \neq 0 \).

### Step 2: Given Condition
We are given that \( x \) and \( y \) are two rational numbers such that \( x > y \). This means that the value of \( x \) is greater than the value of \( y \).

### Step 3: Subtracting the Two Rational Numbers
We need to consider the expression \( x - y \). Since \( x \) is greater than \( y \), we can express this as:
\[ x - y = \text{(a larger number)} - \text{(a smaller number)} \]

### Step 4: Analyzing the Result
When we subtract a smaller rational number \( y \) from a larger rational number \( x \), the result will always be positive. This is because:
- If \( x > y \), then \( x - y > 0 \).

### Step 5: Conclusion
Since \( x - y \) is the difference between two rational numbers where the first is greater than the second, the result \( x - y \) is indeed a positive rational number.

Therefore, the statement is **True**.