Textbook Problem

Define relation R and S on R as follows:

$\begin{array}{l}R=\left\{\left(x,y\right)\in \text{R}\times \text{R|x<y}\right\}\text{and}\\ \text{S=}\left\{\left(x,y\right)\in \text{R}\times \text{R|x=y}\right\},\end{array}$

That is, R is the “less than” relation and S is the “equals” relation on R. Graph $R,S,R\cup S,$ and $R\cap S$ in the in the Cartesian plane.