Suppose that a, b, c, and d are positive numbers with a < b and c

(a) Which of the following statements are consequences of the provided information? Justify or give a

counterexample to each statement.

(i) a+c

(iv) a+c

(ii) a+d

(b) Multiply both sides of the first inequality by c to conclude that ac < bc.

(c) How can you manipulate the second inquality to conclude that bc < bd?

(d) Is it always true that ac < bd? Justify this claim, or provide a counterexample.