Write the Relation as a Set of Ordered Pairs
Question
Write the following relation as the set of ordered pairs:
A relation \(R\) on the set \[ \{1,2,3,4,5,6,7\} \] defined by \[ (x,y)\in R \iff x \text{ is relatively prime to } y. \]
Solution
Two numbers are relatively prime if their HCF is 1.
Therefore,
\[ R= \{ \]
\[ (1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7), \]
\[ (2,1),(2,3),(2,5),(2,7), \]
\[ (3,1),(3,2),(3,4),(3,5),(3,7), \]
\[ (4,1),(4,3),(4,5),(4,7), \]
\[ (5,1),(5,2),(5,3),(5,4),(5,6),(5,7), \]
\[ (6,1),(6,5),(6,7), \]
\[ (7,1),(7,2),(7,3),(7,4),(7,5),(7,6) \} \]