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Q.

If p and q are positive integers, then $p q$ is a rational number and $p − q$ is a rational number and 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.
A positive rational number is the one in which both numerator and denominator have the same sign, i.e., either both are positive or both are negative.
A negative rational number is the one in which the numerator and the denominator have opposite signs, i.e., if the numerator is negative then the denominator is positive or vice-versa.
Based on this fact, we can observe that for the number

p q

, both the numerator and denominator are positive. So, it is a positive rational number.
For the number

p − q

, we can observe that the numerator i.e, p is positive while the denominator i.e., -q is negative.
So, it is a negative rational number.

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