Does Superman exist? (Logical analysis) I am given as exercise to check the following reasonment: "If superman is able to and wants to prevent evil, he will. If superman is not able to prevent evil, then he is passed out. If superman doesn't want to prevent evil, then he is evil. Superman doesn't prevent evil. If Superman exists, he is neither passed out nor evil. Then Superman doesn't exist." I'm a bit uncertain on how to lay out the logical analysis of this.

You have to properly symbolize it; the _premises_ are :

> P1) $(Able_S \land Want_S) \to Prevent_S$
>
> P2) $\lnot Able_S \to Passed_S$
>
> P3) $\lnot Want_S \to Evil_S$
>
> P4) $\lnot Prevent_S$
>
> P5) $Exists_S \to (\lnot Passed_S \land \lnot Evil_S)$

and the sought _conclusion_ :

> > $\lnot Exists_S$.

* * *

Having said that, the sought derivation must be :

1) $\lnot Prevent_S \to (\lnot Able_S \lor \lnot Want_S)$ --- from P1) by Contraposition and De Morgan

2) $\lnot Able_S \lor \lnot Want_S$ --- from 1) and P4) by _modus ponens_

3) $Passed_S \lor Evil_S$ --- from 2), P2) and P3) by Constructive dilemma

4) $(Passed_S \lor Evil_S) \to \lnot Exists_S$ --- from P5) using again Contraposition and De Morgan

> $\lnot Exists_S$ --- from 3) and 4) by _modus ponens_.

* * *

In alternative, you can use Resolution).