cuantificadors lógics

[∀x][ P(x) ] <==> ( P(x_{1} ) ∧...(n)...∧ ( P(x_{n}) )
[∃x][ ¬P(x) ] <==> ( ¬P(x_{1} ) ∨...(n)...∨ ( ¬P(x_{n}) )


[∃x][ P(x) ] <==> ( P(x_{1} ) ∨...(n)...∨ ( P(x_{n}) )
[∀x][ ¬P(x) ] <==> ( ¬P(x_{1} ) ∧...(n)...∧ ( ¬P(x_{n}) )