Symbolizing predicate logic How to symbolize this? 1. Only a pacifist is either a gentlemen or not a fighter. 2. No pacifists are gentlemen if they are fighters. 3. Some members are fighters if and only if they are fighters 4. not all members are fighters.

Here are more logic-like rephrasings of the sentences, which should be easier to translate into first order logic.

1. This means that for anyone $x$ (we'll assume variables range over people), if $x$ is a gentleman or $x$ is not a fighter, then $x$ is a pacifist.

2. For all $x$, if $x$ is a fighter, then if $x$ is a pacifist then $x$ is not a gentleman. More simply: for all $x$, if $x$ is a fighter and $x$ is a pacifist, then $x$ is not a gentleman.

3. I take this to mean: There are $x$ such that $x$ is a member and ($x$ is a fighter if and only if $x$ is a fighter).

4. Not: for all $x$, if $x$ is a member then $x$ is a fighter.




Can you symbolize these, using predicates $Gentleman(x)$, $Fighter(x)$, $Pacifist(x)$, and $Member(x)$?