The value of $\(A=[x+y]\)$ will be $\(x+y\)$ only if $\(x\)$ and $y$ are integers as $\([a]\)$ is defined as the greatest integer less than or equal to $a$. Also $\(B=[x]+[y]=x+y\)$ when $x$ and $y$ are integers. So, values of A \& B will be the same if x and y are integers.

Next if we take non - integer values of $x$ and $y$, we can get different answers. For example taking $\(x=1.2\)$ and $\(y=2.1\)$, we get $\(A=[1.2+2.9]=[4.1]=4 \& B=[1.2]+[2.9]=1+2=3\)$, so the values of column $\(B\)$ may go higher for non-integer values of $\(x\)$ and $\(y\)$.

Hence only option (A) is true.