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
asymmetric if, and only if, for every
intransitive if, and only if, for every
For each of the relations in the referenced exercise, determine whether the relation I irreflexive, asymmetric, intransitive, or none of these.
Exercise 3
To justify whether the relation is irreflexive, asymmetric, intransitive, or none of these.
Given information:
Calculation:
We have:
Irreflexive:
The relation R3 is irreflective if
Since
We note that R3 does not contain