List the Elements of R if R = {(x, y) : x > y} for A = {1, 3, 5} and B = {2, 4}
Question
If
\[ A=\{1,3,5\} \]
and
\[ B=\{2,4\}, \]
list the elements of \( R \), if
\[ R=\{(x,y): x\in A,\ y\in B \text{ and } x>y\} \]
Solution
Checking the pairs:
\[ (1,2)\notin R,\quad (1,4)\notin R \]
\[ (3,2)\in R,\quad (3,4)\notin R \]
\[ (5,2)\in R,\quad (5,4)\in R \]
Therefore,
\[ R=\{(3,2),(5,2),(5,4)\} \]
Hence,
\[ \boxed{\{(3,2),(5,2),(5,4)\}} \]