Unformatted text preview: Yes We must show if (a,b) ∈ R and (b,c) ∈ R, then (a,c) ∈ R. Our assumption leads to the following two equations, based on the definition of R: a = b + 2d , d is an integer b = c + 2e , e is an integer Substitute for b in the first equation to yield: a = (c + 2e) + 2d a = c + 2e + 2d a = c + 2(d+e) Since d and e are both integers, their sum is as well. This means that (a,c) ∈ R. Bonus Question(4 pts): What kind of relation is this? Does this relation partition the set Z + ? If so, how? A equivalence relation. All equivalence relations partition a set. This one has two equivalence classes,  and .  is the set of positive odd integers while  is the set of positive even integers....
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- Fall '09
- Equivalence relation, Binary relation, Transitive relation, Symmetric relation