From Problem $2$ we know that that the logical implication $(EExP(x){)}^{{?}^{?}}(EExQ(x))=>$EEx$[P(x{)}^{{?}^{?}}Q(x)]$ is false. Identify

the error$($s$)$ in the following formal proof that supposedly shows the validity of the following argument

:$.\frac{\text{E}\text{E}\text{x}\text{P}(x{)}^{{?}^{?}}\text{E}\text{E}\text{x}\text{Q}(x)}{\text{E}\text{E}\text{x}[P(x{)}^{{?}^{?}}Q(x)]}$

Step

EExP$(x{)}^{{?}^{?}}$EExQ$(x)$

EExP$(x)$

$P(c)$

EExQ$(x)$

$Q(c)$

$P(c{)}^{{?}^{?}}Q(c)$

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

Reason

Premise

Step $(1)$ and Simplification

Step $(2)$ and Existential Instantiation

Step $(1)$ and Simplification

Step $(4)$ and Existential Instantiation

Steps $(3)$ and $(5)$ and Conjunction

Step $(6)$ and Existential Generalizationrom Problem $2$ we know that that the logical implication $($xP $($x$))($xQ$($x$))$x$[$P $($x$)$ Q$($x$)]$ is false. Identify

the error$($s$)$ in the following formal proof that supposedly shows the validity of the following argument

$$xP $($x$)$xQ$($x$)$

$$x$[$P $($x$)$ Q$($x$)]$

Step Reason

$1.$xP $($x$)$xQ$($x$)$ Premise

$2.$xP $($x$)$ Step $(1)$ and Simplification

$3.$ P $($c$)$ Step $(2)$ and Existential Instantiation

$4.$xQ$($x$)$ Step $(1)$ and Simplification

$5.$ Q$($c$)$ Step $(4)$ and Existential Instantiation

$6.$ P $($c$)$ Q$($c$)$ Steps $(3)$ and $(5)$ and Conjunction

$7.$x$($P $($x$)$ Q$($x$))$ Step $(6)$ and Existential Generalization