Relation from \(A\) to \(B\) Where \(x\) is Relatively Prime to \(y\)
Question
A relation \(R\) is defined from \[ A=\{2,3,4,5\} \] to \[ B=\{3,6,7,10\} \] as follows:
\[ (x,y)\in R \iff x \text{ is relatively prime to } y. \]
Express \(R\) as a set of ordered pairs and determine its domain and range.
Solution
Two numbers are relatively prime if their HCF is 1.
The ordered pairs satisfying the condition are:
\[ R= \{ (2,3),(2,7), \]
\[ (3,7),(3,10), \]
\[ (4,3),(4,7), \]
\[ (5,3),(5,6),(5,7) \} \]
Domain of \(R\):
\[ \boxed{ \{2,3,4,5\} } \]
Range of \(R\):
\[ \boxed{ \{3,6,7,10\} } \]