Question

Define the relation of d on A by xdy if x is contained within y. For
example, 01d101. Draw a digraph for this relation.

Answer 1

 Let a, $b \in Z$ . a b if and only if there exists an integer k such that $a k = b.$

The notation $(4, 16) \in r$ or $(3, 7.2) \in s$ makes sense in both cases. However, r would be more naturally expressed as $r(x) = x^2$ or $r(x)= y$ , where $y = x^2$ . But this notation when used for s is at best awkward. The notation x § y is clear and self-explanatory; it is a better notation to use than $(x,y)\in s$ . Many of the relations we will work with "resemble" the relation $\leq$ , so $x s y$ is a common way to express the fact that x is related to y through the relation s.