Answer:
A) The sum of x and y is a rational number.
Step-by-step explanation:
We will first prove that the given values of x and y are rational and then we will prove the fact that the sum of two rational numbers is a rational number.
A rational number is a number which is in the form [tex]\frac{p}{q}[/tex], where p and q are integers and q ≠ 0.
We can write - 5 as [tex]\frac{-5}{1}[/tex] and clearly 1 ≠ 0.
So, x = -5 is a rational number.
Similarly, y = -4 is also a rational number.
For the second part of the proof, consider any two rational numbers [tex]\frac{p}{q}[/tex] and [tex]\frac{r}{s}[/tex].
Now,
[tex]\frac{p}{q} +\frac{r}{s} =\frac{ps+rq}{qs}[/tex]
Since p, q, r and s are integers, ps + rq is also an integer.
Moreover, since q ≠ 0 and s ≠ 0, qs ≠ 0.
Therefore, [tex]\frac{ps+rq}{qs}[/tex] is also a rational number.
Hence, sum of two rational numbers is also a rational number.
Since x = -5 and y = -4 are rational numbers, x + y = (-5) + (-4) = -9 is also a rational number.
