Answer
Check Work Step by Step Part
Work Step by Step
Given Statement:
The negative of any rational number is rational.
a) ∀real numbers r, if r is a rational number, then -r is also a rational number.
b) The statement is true. Let r be a rational number, then there exist two integer p, q with q ≠0 such that
r = $\frac{p}{q}$ . Now
-r = $\frac{-p}{q}$ = $\frac{p1}{q}$
As p is an integer , p1 = -p is also an integer. Therefore -r is the ratio between two integers with no zero denominators. Hence -r is also rational
