0
$\begingroup$

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.

$\endgroup$
1
$\begingroup$

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.

$\endgroup$
  • $\begingroup$ that helped a lot, I solved it thank you! $\endgroup$ – Anne Jan 31 at 21:42

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.