Chapter 8.2, Problem 48ES

In 43-50, the following definitions are used: A relation on a set A is defined to be Irreflexive if, and only if, for every $x\in A,xRx;$

asymmetric if, and only if, for every $x,y\in A$if $xRy$then $yRx;$

intransitive if, and only if, for every $x,y,z\in A$, if $xRy$and $yRz$then $xRz$.

For each of the relations in the referenced exercise, determine whether the relation I irreflexive, asymmetric, intransitive, or none of these.

Exercise 6