# Proving symmetry and transitivity of a relation

Let R be the relation {(1,1),(1,2),(2,2),(1,3),(3,3)} on the set {1,2,3}.

I am having difficulty proving that it is symmetrical and transitive. I know for symmetry we have to prove if xRy then yRx (if x related to y then y is related to x) and with transitivity we have to show xRy and yRz then xRz. I am having trouble with the set of points and showing that they are or are not symmetrical and transitive. I already proved reflexive because (1,1)R(1,1).

I was thinking if (1,1)R(1,2) then (1,2)R(1,1) --showing symmetry--must be true because those points are in the set, but I think my logic is too simple.

I think you got a bit confused with the different ways to write these things. Here $$xRy$$ is the same thing as $$(x,y)\in R$$. So you have $$1R1,1R2,2R2,1R3,3R3$$. This is the relation. So $$(1,2)\in R$$ but $$(2,1)\notin R$$ which already shows that the relation is not symmetric.