using De Morgan’s negation rule this is equivalent to
⇔ ∄ P ∈X : P is not named Sato
Since X = ∅ is the empty set, such a person P can by definition not exist. Which means, the first statement is true. If no person lives in Japan, that means every person living in Japan is named Sato.
Uh… No? 🤨
∀P∈X : P is named Sato
using De Morgan’s negation rule this is equivalent to
⇔ ∄ P ∈X : P is not named Sato
Since X = ∅ is the empty set, such a person P can by definition not exist. Which means, the first statement is true. If no person lives in Japan, that means every person living in Japan is named Sato.
Your proof is vacuous and you should feel vacuous!
very much so