SOLUTION: Let R be the relation on N defined by the rule that xRy means x + y is not divisible by 6. Is relation R reflexive? Is it symetric? Is it transitive?

Question 1027828: Let R be the relation on N defined by the rule that xRy means x + y is not divisible by 6. Is relation R reflexive? Is it symetric? Is it transitive?
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
It is NOT reflexive: 3R3 is not true (3+3=6 is divisible by 6.)
It is symmetric: If xRy, or (x+y)/6 is not a whole number, then so is (y+x)/6, or yRx.
It is NOT transitive: 3R5 and 5R15 are both true, but 3R15 is not true.
Therefore R is not an equivalence relation.

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