(c)
A salt is precipitated only when the product of ionic concentration is more than its solubility product.
$K_{sp} = 1 \times 10^{- 8}$
$\left\lbrack A^{+} \right\rbrack = 10^{- 3}$ M
$\left\lbrack B^{-} \right\rbrack = \frac{1 \times 10^{- 8}}{10^{- 3}} = 10^{- 5}$ M
So, $AB$ will be more precipitated only when the concentration of $\lbrack B^{-}\rbrack$ is more than $10^{- 5}$ M.