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Somebody Is Not Dead

Some person is dead.
\hspace{5mm} ∃x(Person(x) ∧ Dead(x))
Some person is not dead.
\hspace{5mm} ∃x(Person(x) ∧ ¬Dead(x))
No person is dead.
\hspace{5mm} ¬∃x(Person(x) ∧ Dead(x))
Every person is dead.
\hspace{5mm} ∀x(Person(x) → Dead(x))
Every person is not dead.
\hspace{5mm} ∀x(Person(x) → ¬Dead(x))
Not every person is dead.
\hspace{5mm} ¬∀x(Person(x) → Dead(x))

Some person is dead.

∃x(Person(x) ∧ Dead(x))

Some person is not dead.

∃x(Person(x) ∧ ¬Dead(x))

No person is dead.

¬∃x(Person(x) ∧ Dead(x))

Every person is dead.

∀x(Person(x) → Dead(x))

Every person is not dead.

∀x(Person(x) → ¬Dead(x))

Not every person is dead.

¬∀x(Person(x) → Dead(x))

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