# Characteristics of relations. Are these relations correct?

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.

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

• 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. – fleablood Jul 6 '16 at 5:55
• Great, thanks, I made a mistake only meant to add 3 questions. Accidentally repeated 2. – Kazu Jul 6 '16 at 6:05
• 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. – pjs36 Jul 6 '16 at 6:21
• 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. – fleablood Jul 6 '16 at 6:30

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.