Answer Happy

4. (25 points) For each of the following relations, determine if it is an equivalence relation. If it is an equivalence relation, give two elements in the indicated equivalence class [s]. If it is not an equivalence relation, indicate which rule it does not satisfy (if there is more than one rule broken you only need to indicate one, but be sure to justify your answer). (a) (8 points) Let A be Z, and say (m,n) E R if a +b = 0 mod 2. Here s = 5. (b) (8 points) Let A be the set of all points in two dimensions. We say ((1,yı), (12, y2)) e Rif xi +xz> y + yž. Let s = (1,1). (c) (9 points) Let A be the set of all functions from R to R, and we define (8,9) € R if (0)g(0) > 0. Let s = 12 +1.