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.
But it does though
“Every person in Japan will be called Sato.”
In formal logic, this is equivalent to
“There is no person in Japan not called Sato.”
Since there are no people, no one is not called Sato, and therefore every person is called Sato. Every person is also called Steve. Or Klaus.
Edit: once you take the second part of the headline about the marriage law into account you’re right, my bad -
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