Question $2\mathrm{.}4$

Using the basic natural deduction rules for predicate logic, prove the validity of the following sequent:

$($i$),$AAx$(P(x{)}^{{?}^{?}}Q(x)),$EEyS$(y)|--$EEz$(P(z{)}^{{?}^{?}}S(z))$

$($ii$)$ AAx$(P(x)(Q(x)vvR(x))),$notEEx$(P(x{)}^{{?}^{?}}R(x))|--$AAx$(P(x)Q(x))$