$I$. Magnesium hydroxide is a strong base.
$II$. Hydroxides of alkali metals and most alkaline earth metals are strong bases.

The correct option is C Statement $I$ is false, Statement $II$ is true
As $Mg(OH{)}_2$ is less soluble in water, it is a weak base, but alkali metal bases and most of the alkaline metals bases are strong.

As we go down the group, the strength of the hydroxide of alkali metal and alkaline earth metal increases.