For 1, suppose that x is irrational, that p is rational and q = p - x. Either q is rational or irrational. If q is rational then p - q is rational which would imply that x is rational. By contradiction, then p - x must…
For 1, suppose that x is irrational, that p is rational and q = p - x. Either q is rational or irrational. If q is rational then p - q is rational which would imply that x is rational. By contradiction, then p - x must…