How do I proof this?

**TheRekz** · June 19th 2007, 01:12 PM

Show that the $\left( {\forall x} \right)$ P(x) V $\left( {\forall x} \right)$ Q(x) and $\left( {\forall x} \right)$ (P(x) v Q(x)) are not logically equivalent.

How do I proof this just using an example?? Thanks

**Plato** · June 19th 2007, 01:47 PM

$\left( {\forall y} \right)\left[ {R(y)} \right]$ means everyone here is Russian.

$\left( {\forall z} \right)\left[ {E(z)} \right]$ means everyone here is English.

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

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