Let R be the relation on Z (the set of integers) defined by (x, y)  R iff x 2 + y2 = 2k for some integers k  0. Answer questions 13 to 15 by using the given relation R. Question 13 Which one of the following is an ordered pair in R? 1. (1, 0) 2. (2, 9) 3. (3, 8) 4. (5, 7) Question 14 R is symmetric. Which one of the following is a valid proof showing that R is symmetric? 1. Let x, y  Z be given. Suppose (x, y)  R then x 2 + y2 = 2k for some k  0. ie y 2 + x2 = 2k for some k  0. thus (x, y)  R. 2. Let x, y  Z be given. Suppose (x, y)  R then x 2 + y2 = 2k for some k  0. ie y 2 + x2 = 2k for some k  0. thus (y, x)  R. 3. Let x, y  Z  be given. Suppose (x, y)  R then x 2 + y2 = 2k for some k  0. thus (y, x)  R. 4. Let x, y  Z be given. Suppose (x, x)  R then x 2 + y2 = 2k for some k  0. ie y 2 + x2 = 2k for some k  0. thus (y, y)  R.