1. Let S = {a, b, c, d, e} and define the equivalence relation R = {(a, a), (b, b), (c, c), (d, d), (e, e), (a, c), (c, a)}. Describe the partition p determined by R by listing the pieces in p
2. Let S = {a, b, c, d, e} and define the equivalence relation R = {(a, a), (b, b), (c, c), (d, d ), (e, e), (a, b), (b, a), (a, d ), (d, a), (b, d ), (d, b)}. Describe the partition p determined by R by listing the pieces in p
3. Define a relation R on the set of all integers Z by x R y iff x – y = 2k for some integer k. Verify that R is an equivalence relation and describe the equivalence class E5. How many distinct equivalence classes are there?