Let $A = \{ 3,5,7 \}$ And $B = \{ 15,16,17,18 \}$

Essay

Let $A = \{ 3,5,7 \}$ and $B = \{ 15,16,17,18 \}$ , and define a relation $R$ from $A$ to $B$ as follows: For all $( x , y ) \in A \times B$ ,
$( x , y ) \in R \quad \Leftrightarrow \quad \frac { y } { x }$ is an integer.
(a) Is $3 R 15$ ? Is $3 R 16 ? \quad$ Is $( 7,17 ) \in R$ ? Is $( 3,18 ) \in R$ ?
(b) Write $R$ as a set of ordered pairs.
(c) Write the domain and co-domain of $R$ .
(d) Draw an arrow diagram for $R$ .
(e) Is $R$ a function from $A$ to $B$ ? Explain.