
Thus R = {(1, 1), (1, 3), (2, 2), (2, 4), (3, 3), (3, 1), (4, 4), (4, 2)}. Since there are eight pairs in R,
there will be eight arrows in the digraph.
2
4
1
3
When a set is very large, digraphs and roster notation are not very useful. In this case a theoretical
description of the relation is handier.
Exercises
1. Consider the function f : ℝ→ℝ defined as f (x)=3x
2
+1. On ℝ define the relation “a is in relation with
b if and only if f (a)=f (b).” Find which numbers are in relation.
2. Consider the set A ={−3, −2, −1, 0, 1, 2, 3}. On A define the relation R as “a i s in relation with b
if and on ly if |a|=|b|.” Find which elements of A are i n relation and ...