Can I rewrite the sentence "everybody loves somebody" as follows:
∀x(Person(x) -> ∃y(Person(y) ^ Loves(x,y)))
Can I rewrite the sentence "everybody loves somebody" as follows:
∀x(Person(x) -> ∃y(Person(y) ^ Loves(x,y)))
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Sure, let $Lxy$ be the predicate 'x loves y':
$(\forall x)(\exists y)(Lxy)$