do both of the questions

4. (Ch. 2.3, an exercise out of the blue) Determine whether each of the relations R below defined on Z antisymmetric, and/or transitive. is reflexive symmetrie (a) I~ y(or (I, Y) E R) if 3 divides 1 + 2y. (b) 2~y (or (1, y) E R) if I - y = 2. 5. (Ch. 0, Review Exercise 12 on p. 18 of our text) The number T = LYS is called the golden mean. The ancient Greeks felt that a rectangle whose sides were in the ratio of 1 tot was! the most esthetically pleasing. Such a rectangle is called golden. Hence, for example, cach side of the Parthenon, a large rectangular building dating to 435 B.C. is a golden rectangle. Suppose you remove a 1x1 square from a golden rectangle (as illustrated in the text on! 18). Prove that the rectangle that remains is golden