TITLE: Is the given relation transitive?
QUESTION [8 upvotes]: Consider the relation:
$$R = \{(a,b), (a,c), (c,c), (b,b), (c,b), (b,c)\}$$ on the set $A = \{a,b,c\}$. Is $R$ transitive? I said no because
$$[(c, c) \wedge (a, c)] \Longrightarrow (c,a)$$ is a false statement. Is my reasoning correct?

REPLY [13 votes]: When unsure about this things, make a drawing:

Transitivity means that if you can get somewhere through some route (for example, from $a$ to $c$ doing $a\to b\to c$) you must be able to get there directly ($a\to c$).
I hope this is easily seen in the drawing.