I have problem to understand the equivalence of the following sentence intuitively for long time
∀x.(px=>q)
∃x.px=>q
I understand the truth table below does says they are equivalent:
p(a) p(B) q p(a)=>q p(b)=>q (p(a)=>q)&(p(b)=>q) p(a)|p(b) p(a)|p(b) =>q
T F T T T T T T
F T T T T T T T
T T T T T T T T
F F T T T T F T
T F F F T F T F
F T F T F F T F
T T F F F F T F
F F F T T T F T
But what i'm looking for is an human language example to verify the validity of the equivalence, so I could understand more intuitively, could anyone give a example?
The second one means "there is a px value which implies a q result".
The first one means "for each px value, there is a q result"
This could be the difference between "a driver has a driving licence" and "every drivers must have one".