Originally Posted by

**Plato** No that is not correct. But I will say that this one is very tricky.

$\displaystyle \begin{gathered}

(x,x + 1) \in R_3 \,\& \,\left( {x + 1,x} \right) \in R_1 \Rightarrow \quad \left( {x,x} \right) \in R_1 \circ R_3 \hfill \\

x < y \Rightarrow \quad \left( {x,y + 1} \right) \in R_3 \,\& \,\left( {y + 1,y} \right) \in R_1 \Rightarrow \quad \left( {x,y} \right) \in R_1 \circ R_3 \hfill \\\end{gathered}$

$\displaystyle x > y \Rightarrow \quad \left( {x,x + 1} \right) \in R_3 \,\& \,\left( {x + 1,y} \right) \in R_1 \Rightarrow \quad \left( {x,y} \right) \in R_1 \circ R_3

$

Does this show that every pair it there?