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Question: 5 s4 s5 let a 12 34 56 we...

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5. (S4, S5) Let A - [1,2, 3,4, 5,6). We define relation R on set A as follows: (x,y) є R if and only if 3 divides x-y Recall, when we say one number divides another, we mean that it divides it perfectly without a remainder (a) Draw the directed graph of relation R on the setA (b) Explain in your own words why R is reflexive, symmetric, and transitive. (c) If a relation on a set is reflexive, symmetric, and transitive, we call it an equivalence relation which splits the elements of the original set into separate non-overlapping families of related elements called equivalence classes. Can you identify these separate equivalence classes for relation R? d) Why do you think the term equivalence relation is used to describe such a relation? In what ways might this term seem appropriate?

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