# "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." #