Write Relation as Ordered Pairs and Check Whether it is a Function
Question:
$$
\{(x,y): y>x+1,\ x=1,2 \text{ and } y=2,4,6\}
$$
Solution
For \(x=1\),
$$ y>1+1 $$
$$ y>2 $$
So, \(y=4,6\)
Ordered pairs are:
$$ (1,4),\ (1,6) $$
For \(x=2\),
$$ y>2+1 $$
$$ y>3 $$
So, \(y=4,6\)
Ordered pairs are:
$$ (2,4),\ (2,6) $$
Therefore,
$$ R=\{(1,4),(1,6),(2,4),(2,6)\} $$
Since one element has more than one image, the relation is not a function.
$$ \boxed{\text{The relation is not a function.}} $$