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 ∈ A ,   x R x ;

asymmetric if, and only if, for every x , y ∈ A if x R y then y R x ;

intransitive if, and only if, for every x , y , z ∈ A , if x R y and y R z then x R z .

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

Exercise 8