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Relations: Transitivity

A \emph{transitive} relation is one such that if x bears it to y and y bears it to z then x bears it to z. (E.g. LeftOf is transitive; NotAdjacent is not transitive.)
\begin{minipage}{\columnwidth}
If NotAdjacent were transitive, the following argument would be logically valid:
\end{minipage}
\begin{minipage}{\columnwidth}
A counterexample to this argument:
\end{minipage}

express the counterexample formally

 

Domain

{0, 1, 2}

Names

a : 0

b : 1

c : 2

Predicates

NotAdjacent : {

<0,1>, <1,2>,

<1,0>, <2,1>

}

 

Domain

{0, 1, 2}

Names

a : 0

b : 1

c : 2

Predicates

NotAdjacent : {

<0,1>, <1,2>,

<1,0>, <2,1>

}

 

Domain

{0, 1, 2}

Names

a : 0

b : 1

c : 2

Predicates

NotAdjacent : {

<0,1>, <1,2>,

<1,0>, <2,1>

}