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E(x) = x is Earthling

A(x) = x is Alien

What is the corresponding Well Formed Formula for "Nobody is Earthling unless somebody is Alien" ?

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Nobody is Earthling unless somebody is Alien

"A unless B" in predicate logic is $\sim B \rightarrow A$

A = "Nobody is Earthling" or $\sim \exists x(Earthling(x))$

B = "somebody is Alien" or $\exists x(Alien(x))$

$\sim B \rightarrow A$ 

$\sim \exists x(Alien(x)) \rightarrow \sim \exists x(Earthling(x))$ 

or $\forall x(\sim (Alien(x))) \rightarrow \forall x(\sim (Earthling(x)))$ 

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Nobody is Earthling unless somebody is Alien

we can write it like this

If somebody is not Alien then nobody is earthling

$\exists x(\sim A(x))\rightarrow \sim( \forall (x)E(x))$

for ref see: Rosen Exercise-1 19 h) 

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