$\backslash$table$[[$Entered$,$Answer Preview,Result$],[$GIVEN$,$GIVEN,incorrect$],[$EXISTENTIALINSTANTIATION$,1,$EXISTENTIALINSTANTIATION, $1,$correct$],[$SIMPLIFICATION$,2,$SIMPLIFICATION, $2,$correct$],[$R$($C$),$R$($C$),$incorrect$],[$P$($C$),$P$($C$),$incorrect$],[$UNIVERSALINSTANTIATION$,$ AAx$($P$($x$)->$Q$($x$)),$UNIVERSALINSTANTIATION, AAx$($P$($x$)->$Q$($x$)),$incorrect$],[$Q$($C$),$Q$($C$),$incorrect$],[$REPETITION$,7,$REPETITION,$7,$incorrect$],[$REPETITION$,4$AND$5,$REPETITION, $4$AND$5,$incorrect$],[$R$($C$)^^$Q$($C$),$R$($C$)^^$Q$($C$),$correct$],[$CONJUNCTION$,3$AND$6,$CONJUNCTION, $3$AND$6,$incorrect$],[$EXISTENTIIALGENERALIZATION$,7,$EXISTENTIIALGENERALIZATION,$7,$incorrect$]]$ Complete the logical proof for the following argument.

AAx$(P(x)Q(x))$

EEx$(R(x{)}^{{?}^{?}}P(x))$

:$.$EEx$(R(x{)}^{{?}^{?}}Q(x))$

$\backslash$table$[[$Step$,$Proposition,Justification$],[1,$EEx$($R$($x$)^^$P$($x$)),$Given$],[2,$c is a specific element $^^($R$($c$)^^$P$($c$)),$Existential Ins tan tiation, $1],[3,$c is a specific element,Simplification, $2],[4,$R$($c$),$Simplification, $2],[5,$P$($c$),$Hypothesis$],[6,$P$($c$)->$Q$($c$),$Simplification, $4],[7,$Q$($c$),$Repetition, $7],[8,$Q$($c$),$Repetition, $4$ and $5],[9,$EE$($c$),$Conjunction, $3$ and $6],[10,$R$($c$)^^$Q$($c$),$Existentiial Generalization, $7],[11,$EEx$($x$)^^$Q$($x$)),]]$

Note that the justification for each step is either hypothesis or it would include both the name of the law or rule and the step$($s$)$ to which it is applied to$.$

Copy and paste the logical operators when filling in the blanks: $vv,{?}^{{?}^{?}},,$not,$AA,EE.$