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      -22 months ago

      ∀P∈X X lives in Japan : P is named Sato

      using De Morgan’s negation rule this is equivalent to

      ⇔ ∄ P ∈X X lives in Japan : P is not named Sato

      Since X X lives in Japan = ∅ 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.