Domain of a Relation | Relatively Prime Relation
Question
A relation \( R \) is defined from \( \{2,3,4,5\} \) to \( \{3,6,7,10\} \) by
\[ xRy \iff x \text{ is relatively prime to } y \]
Then, domain of \( R \) is
(a) \( \{2,3,5\} \)
(b) \( \{3,5\} \)
(c) \( \{2,3,4\} \)
(d) \( \{2,3,4,5\} \)
Solution
\(2\) is relatively prime to \(3\) and \(7\).
\(3\) is relatively prime to \(7\) and \(10\).
\(4\) is relatively prime to \(3\) and \(7\).
\(5\) is relatively prime to \(3\), \(6\) and \(7\).
Thus every element of \[ \{2,3,4,5\} \] is related to at least one element of the second set.
Hence, \[ \text{Domain of }R=\{2,3,4,5\} \]
Therefore, the correct answer is (d).