Answer
$div (F+G)=div F+div G$
Work Step by Step
Suppose $F=ai+b j$
$div F=\dfrac{\partial a}{\partial x}+\dfrac{\partial b}{\partial y}$
Suppose $F=a_1i+b_1j; G=a_2i+b_2j$
Now, $div (F+G)=\dfrac{\partial a_1}{\partial x}+\dfrac{\partial b_1}{\partial y}+\dfrac{\partial a_2}{\partial x}+\dfrac{\partial b_2}{\partial y}$
Hence, we get $div (F+G)=div F+div G$
