suppose that p and q are rational numbers and r is an irrational number
If p and q are rational numbers, it means that they can be expressed as fractions of two integers. Let's say p = a/b and q = c/d, where a, b, c, and d are integers and b, d ≠ 0.
On the other hand, an irrational number cannot be expressed as a fraction of two integers. So, r cannot be written as r = e/f, where e and f are integers and f ≠ 0.
In general, p, q, and r are distinct types of numbers with different properties. Rational numbers can be expressed as fractions, whereas irrational numbers cannot.