8. (14 points) Write negations for each of the following sentences by using the equivalence ~(p → q) ≡ p ∧ ~q and De Morgan's laws. (Assume that all variables represent fixed quantities or entities, as appropriate.)
(a) If P is a square, then P is a rectangle.
(b) If today is New Year's Eve, then tomorrow is January.
(c) If the decimal expansion of r is terminating, then r is a rational number.
(d) If n is a prime, then n is odd or n is 2.
(e) If x is nonnegative, then x is positive or x is 0.