Write the Relation \(R\) in Roster Form
Question
\[ A=\{1,2,3,5\} \]
and \[ B=\{4,6,9\} \]
Define a relation \(R\) from \(A\) to \(B\) by
\[ R=\{(x,y): \text{the difference between } x \text{ and } y \text{ is odd},\ x\in A,\ y\in B\} \]
Write \(R\) in roster form.
Solution
Difference is odd when one number is even and the other is odd.
Checking the ordered pairs:
\[ (1,4),(1,6) \]
\[ (2,9) \]
\[ (3,4),(3,6) \]
\[ (5,4),(5,6) \]
Therefore,
\[ \boxed{ R= \{ (1,4),(1,6), (2,9), (3,4),(3,6), (5,4),(5,6) \} } \]