Determining if logically equivalent

[daring chasm]

having issues with this type of problem

like i get to simplifying them, but idk what to do....

[sturdy grotto]

I would consider a concrete example of P and Q and see how it reads.

[radiant kraken]

I am not very good in demonstrations but since at first it says: « for any x taken, P(x)=>Q(x)» so it is fair that the second statement is equivalent: « for any x taken P(x)=> Q(x) for any x taken »

I may be saying nonsense which is most likely but I am willing to try to understand

[vocal spruce]

Yeah

[daring chasm]

didnt understand a single word

[radiant kraken]

I can understand why…good luck for your problem though !

[normal sonnet]

it's not generally true

for reference, see distribution scheme

to prove second order logic schemes from semantics model conditions, you need to translate semantic axioms into logical schemes

[vocal spruce]

Think of specific examples

The first one means P(x) implies Q(x) for all x

So for both P and Q it will always be the same x

But the second one says that if P(x) is true for all x, then Q(x) is also true for all x

The first one is just if P(x) is true then Q(x) is true for any given x

So if we take the first statement to be true
Then whenever P(x) is true, Q(x) is true
If we take the second statement to be true
Whenever P(x) is true for ALL x, Q(x) is true for ALL x