A relation R on a set A is called transitive if whenever (a,b)∈R and (b,c)∈R, then (a,c)∈R, for all a,b,c∈A
If we consider the relation R that contains (x,y) if x is older than y on the set of all students in the class, then we know that if (x,y)∈R and (y,z)∈R, then (x,z)∈R
This can be formalised in predicate logic by
Where the domain is the set of all elements in A