Chapter 1.3, Problem 7ES

Let $A=\left\{4,5,6\right\}$ and $B=\left\{5,6,7\right\}$ and define relations R,S, and T from A to B as follows:

For every $\left(x,y\right)\in A\times B:$

$\left(x,y\right)\in R$ means that $x\ge y$ .

$\left(x,y\right)\in S\text{means}\text{that}\frac{x-y}{2}\text{is}\text{an integer}\text{.}$

$T=\left\{\left(4,7\right),\left(6,5\right),\left(6,7\right)\right\}.$

1. Draw arrow diagrams for R, S, and T.
2. Indicate whether any of the relations R, S, and T are functions.