Write the Relation as a Set of Ordered Pairs
Question
Write the following relation as the set of ordered pairs:
A relation \(R\) from the set \[ A=\{5,6,7,8\} \] to the set \[ B=\{10,12,15,16,18\} \] defined by \[ (x,y)\in R \iff x \text{ divides } y. \]
Solution
\[ 5\mid10,\quad 5\mid15 \]
\[ (5,10),(5,15) \]
\[ 6\mid12,\quad 6\mid18 \]
\[ (6,12),(6,18) \]
\[ 7 \] does not divide any element of \(B\).
\[ 8\mid16 \]
\[ (8,16) \]
Therefore,
\[ \boxed{ R= \{ (5,10),(5,15), (6,12),(6,18), (8,16) \} } \]