"We are given a relation, call it" \ R:"
\qquad \qquad \qquad \qquad \qquad R \ = \ { (1, 0), (2, 0), (3, 0), (4, 0) }.
"1) Recall that the domain of a relation is the set of all first"
"coordinates of the ordered pairs in the relation. So:"
\qquad \qquad \qquad \qquad \qquad \qquad "domain of" \ \ R \ = \ { 1, 2, 3, 4 }.
"2) Recall that the range of a relation is the set of all second"
"coordinates of the ordered pairs in the relation. So:"
\qquad \qquad \qquad \qquad \qquad \qquad \ "range of" \ \ R \ = \ { 1, 2, 3, 4 }
\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ = \ { 0 }.
\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad "(remember to simplify the set;"
\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad "duplicate entries must be removed)"
"3) Recall that a relation is a function precisely when the first"
"coordinates of the ordered pairs in the relation contain no"
"repetitions. Scanning the first coordinates of the ordered pairs"
"of" \ \ R, \ "we see that none of them occur repeated. Each first"
"coordinate occurs only once !! Thus:"
\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ \ R \ \ "is a function."
