Define a relation R on the set of all integers Z by x R y iff x + y = 3 k for some integer k. Is R an equivalence relation on Z? Why or why not? (Compare with Exercise 24.) Exercise 24 Define a...

Define a relation R on the set of all integers Z by x R y iff x + y = 3 k for some integer k. Is R an equivalence relation on Z? Why or why not? (Compare with Exercise 24.)

Exercise 24

Define a relation R on the set of all integers Z by x R y iff x – y = 3k for some integer k. Verify that R is an equivalence relation and describe the equivalence class E₅. How many distinct equivalence classes are there?