
How do I proof this?
Show that the $\displaystyle \left( {\forall x} \right)$ P(x) V $\displaystyle \left( {\forall x} \right)$ Q(x) and $\displaystyle \left( {\forall x} \right)$ (P(x) v Q(x)) are not logically equivalent.
How do I proof this just using an example?? Thanks

$\displaystyle \left( {\forall y} \right)\left[ {R(y)} \right]$ means everyone here is Russian.
$\displaystyle \left( {\forall z} \right)\left[ {E(z)} \right]$ means everyone here is English.
$\displaystyle \left( {\forall x} \right)\left[ {R(y) \vee E(x)} \right]$ means everyone here is Russian or English.