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## Main Question or Discussion Point

Having trouble understanding the concept of transitivity.

By definition: If [itex](a,b)\in R\wedge (b,c)\in R \Rightarrow (a,c)\in R[/itex] - Great.

Consider the set [itex]\{a,b\}[/itex]. What makes the relation [itex]\{(a,a)\}[/itex] or [itex]\{(a,a),(a,b)\}[/itex] transitive? How do I translate this in terms of the definition?

What makes an empty set transitive?

By definition: If [itex](a,b)\in R\wedge (b,c)\in R \Rightarrow (a,c)\in R[/itex] - Great.

Consider the set [itex]\{a,b\}[/itex]. What makes the relation [itex]\{(a,a)\}[/itex] or [itex]\{(a,a),(a,b)\}[/itex] transitive? How do I translate this in terms of the definition?

What makes an empty set transitive?