There is relation
$$R=\left\{(1,1),(1,5),(2,4),(3,3),(4,1),(4,2),(5,4)\right\}$$
What properties (see title) it have?
Hi maths people I learn for test next week. Here is my idea is it good or not?
-not reflexive because we don't have $(2,2)$ as example
-not irreflexive because we have for example $(1,1)$
-not symmetric because for example $(1,5)$ exists but no $(5,1)$
-not asymmetric because for example $(2,4)$ and $(4,2)$ exist
-not antisymmetric because for example $(2,4)$ and $(4,2)$ exist but they are not equal
But no idea is transitive very complicated.. Is trick to check it easy pls tell me?
And is my reasons good and correct?
Best Answer
All your answers (and reasons given!) so far are correct!
Transitivity means that whenever you have $(a,b)$ and $(b,c)$, you should also have $(a,c)$. What do you think: do you have that here?