If the relation $R:A\to B$ , where $A=\left\{1,2,3\right\}$  and $B=\left\{1,3,5\right\}$  is defined by $R=\left\{\left(x,y\right):x<y,x\in A,y\in B\right\}$ , then

Since, $R=\left\{\left(x,y\right):x<y,x\in A,y\in B\right\}$

i.e., R contains all those pairs for which the first number from the set $A$  is less than the second from the set B.  Only option (A) is correct.