PREDICATE LOGIC DOUBT 3

Question

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" ?

Comments

@Balaji

where u got the question?

Can u see once Rosen plz

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srestha Question is a self doubt. A similar question is there in The Power of Logic by Daniel Howard-Snyder, Frances Howard-Snyder & Ryan Wasserman.

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Balaji plz chk ans and see anything mistake

Answer 1

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

Comments

this is the way

Answer 2

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) 

Comments

check this