PREDICATE LOGIC DOUBT 2

Question

Nothing is Earthling unless it is not Alien

A(x) = x is Alien

E(x) = x is Earthling

Which of the following is correct?

1. (∀x)(~A(x) -> E(x))

2. (∀x)(E(x) -> ~A(x))

3. (∀x)(~A(x) <-> E(x))

Comments

"Nothing is Earthling unless it is not alien" means that only if it is not an alien, then only it is an earthling.

So this means that ~A(X)->E(X) (if it is not an alien, then it is an earthling) and  E(X)->~A(X) (If it is an earthling, then it is not an alien) ,for all X.

So option 3 is correct.

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Answer given is Option 2.

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if u will take true case in option 3 then it will result as x is not alien and x is earthing bt its is not correct as if x is not alien then it may or may not be earthing bt if it is earthing then it should not be alien ..

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Yes.. I got my mistake.. If it is an earthling, then it is not an alien but if it isn't an alien doesn't imply that it is an earthling or not. So option 2 is correct.

Answer 1

Nothing is Earthling unless it is not Alien means if it is earthing then it should not be alien bt if not alien then it may or may not be earthing .. 

so (∀x)(E(x) -> ~A(x)) {if earthing then not alien is correct answer}

option 2 is correct