Question

Increasing the two objects will cause the gravitational force between the objects to decrease.

Answer 1

Well first, I don't quite understand how you can "increase two objects".
I mean, you can increase their size, density, mass, weight, or cost,
but how do you "increase" the objects ?

If you were to, say, increase their mass ... or even the mass of only
one of them ... then the gravitational forces between the objects would
increase in strength.

So if you meant to say "increasing the mass of two objects", then
you've got yourself a nice genuine false statement there. 

Answer 2

This statement is false. Increasing the two objects' mass (I'm guessing) will actually increase their gravitational force. This is because of the equation:

$F_g = \frac{Gm_1m_2}{d^2}$

If the distance was increased, then the statement would be true, but since you are increasing mass, which is proportional to the Force of Gravity, you are in fact, increasing the gravitational force between the two objects.