Let a, b, c, d R and consider each of the following statements. Decide which are

Question:

Let a, b, c, d ∈ R and consider each of the following statements. Decide which are true and which are false. Prove the true ones and give counterexamples to the false ones.
a) If a < b and c < d < 0, then ac > bd.
b) If a < b and c > 1, then |a + c| < |b + c|.
c) If a < b and b < a + c, then |a - b| < c.
d) If a < b - s for all E > 0, then a < 0.