Define a relation R on the set of all integers by xRy iff x + y = 2k for some integer k. Is R an equivalence relation on ? Why or why not? (Compare with Exercise 23.)
Compare with Define a relation R on the set of all integers by xRy 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?
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