Hmm, does this mean that your textbooks only gives examples of transitive relations, without proofs that they are actually transitive? If there are proofs or explanations, then those are arguments... Does your textbook have the definition of transitivity?

A relation on a set is called transitive if for all , if and , then .

To show that a relation is transitive you need to thoroughly understand this definition, and you need to know how to prove statements of the form "for all x, ..." and "if ..., then ...".