Range of a Relation | Relation from A to B
Question
If \( A=\{1,2,3\} \), \( B=\{1,4,6,9\} \) and \( R \) is a relation from \( A \) to \( B \) defined by “\( x \) is greater than \( y \)”. Then the range of \( R \) is
(a) \( \{1,4,6,9\} \)
(b) \( \{4,6,9\} \)
(c) \( \{1\} \)
(d) none of these
Solution
Relation is defined by \[ x>y \] where \( x\in A \) and \( y\in B \).
Checking elements:
\[ 2>1 \Rightarrow (2,1) \]
\[ 3>1 \Rightarrow (3,1) \]
No other element of \( B \) is less than elements of \( A \).
Therefore, \[ R=\{(2,1),(3,1)\} \]
Range of \( R \) is \[ \{1\} \]
Hence, the correct answer is (c) \( \{1\} \).