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If p and q are positive integers, then $p q$ is a rational number and $p − q$ is a rational number.

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Detailed Solution

If p and q are positive integers, then

p q

is a positive rational number and

p − q

is a negative rational number.
If a number can be represented in the form

p q

, a number is considered rational, where

p

and

q

are integers and

q

is not equal to zero.
A positive rational number is expressed as

p q

and a negative rational number is expressed as

p − q

.
Therefore, if p and q are positive integers, then

p q

is a positive rational number and

p − q

is a negative rational number.

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