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The question asks: Let $A= \{1,2,3\}$. List the ordered pairs and draw the digraph of a relation on $A$ with the given properties. I just want to check if my ordered pairs are correct or not so I have no doubts.

  1. reflexive, not symmetric, and not transitive.

$$\{(1,1),(2,2),(3,3),(1,3),(2,3)\}$$

  1. not reflexive, symmetric, and not transitive.

$$\{(1,1),(2,2),(3,1),(1,3)\}$$

  1. reflexive, symmetric, and not transitive.

$$\{(1,1),(2,2),(3,3),(1,2),(2,1)\}$$

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  • $\begingroup$ a relation with the properties. Not all? All yours are good (and there are others, of course). Um... what's the difference between 2 and 3? But yes, your relations are all correct. $\endgroup$ – fleablood Jul 6 '16 at 5:55
  • $\begingroup$ Great, thanks, I made a mistake only meant to add 3 questions. Accidentally repeated 2. $\endgroup$ – Kazu Jul 6 '16 at 6:05
  • $\begingroup$ Why exactly aren't the 1st and 3rd transitive? They might not be, but I don't see any ordered pairs that are "missing" so as to violate transitivity. $\endgroup$ – pjs36 Jul 6 '16 at 6:21
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    $\begingroup$ oops, @pjs36 is right. All of these are transitive. Replace (2,3) with (32) and 1) is good (As 1 R 3 and 3 R 2 but 1 not R 2). Add (3,2) and (2,3) to the 2nd and you have 1 R 3 and 3 R 2 but 1 not R 2. ditto the last. $\endgroup$ – fleablood Jul 6 '16 at 6:30
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All of your answers are correct besides the very first one. Looking at the first one, I cannot spot any instance where the ordered pairs are $not$ transitive. Hence it must be transitive. Other than that, the rest are fine.

EDIT: The last answer is also transitive as the comment below pointed out. Thank you for spotting the error.

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  • $\begingroup$ As the Comments on the Question pointed out, the third relation is also transitive, but described by the OP as not transitive. $\endgroup$ – hardmath Apr 15 '18 at 23:36

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