We have two sets $\(X=\{1,2,3,4,5\} \& Y=\{11,12,13,14,15\}\)$; we need to find the number of different sums that can be obtained if one number is selected from set X and the other one is selected from set Y.

The minimum and the maximum sums that can be obtained by adding one element from set X and the other one from set $Y$ is $\(1+11=12 \& 5+15=20\)$ respectively.

So, all the values from $\(12 \& 20\)$, both inclusive, can be obtained by adding the values of set X and set Y.

Hence a total of $\(20-12+1=9\)$ different sums can be obtained, so the answer is (B).