Answer
This statement is false.
Work Step by Step
The solubility product is simply a K value (an equilibrium constant) to describe how much a salt will dissolve. The fact that there is already a common ion is present will only change how much of the salt will dissolve. K is only affected by temperature, so while the amount of the salt that will dissolve may change, the presence of the common ion will not change the solubility product.
