# First Order Logic, Translation an english sentence

"Between all the animals, Paul loves all tigers and no lions"

Which one is correct?

1) $\forall x$ Animal(x) $\Rightarrow$ (Loves(Paul,x)$\Rightarrow$($\neg$ Lion(x) $\land$ Tiger(x))

2)$\forall x$ Animal(x) $\Rightarrow$ ((Lion(x) $\Rightarrow$ $\neg$Loves(Paul,x)) $\land$(Tiger(x) $\Rightarrow$ Loves(Paul,x))

3)$\forall x$ (Animal(x) $\Rightarrow$ (Tiger(x) $\Rightarrow$ Loves(Paul,x))

I would think that is the second one but i rode somewhere that this form where predicates are replicated twice negated is not so good. So for exclusion it might be the 1).

Actually the first one use Loves as premise, instead the second one use it as conclusion !

Am i right?

Thanks

• @ZhaledAsufian: If $\mathit{Loves}(\cdots)$ is always false, then $\mathit{Loves}(\cdots)\Rightarrow\cdots$ is always true, and then $\cdots\Rightarrow(\mathit{Loves}(\cdots)\Rightarrow\cdots)$ is always true too. Check the truth table for $\Rightarrow$. – hmakholm left over Monica Oct 1 '17 at 12:30