Question B1: Suppose that a, b, c, and d are positive numbers with a < b and c < d. (a) Which of the following statements are consequences of the provided information? Justify or give a counterexample to each statement. (i) a+c<b+c (ii) a+d<c+d (iii) b+c<c+d (iv) a+c<b+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.