Some of us happen to like straw men thank you very much.
Fine, fine Lost, we'll get all technical if we must.
P1 => If a person is a pirate, they are not a ninja.
P2 => No one who is a ninja can be a pirate.
P3 => All people who wear all black and carry swords or claws or throwing stars are ninjas with self-inflicted super powers.
P4 => All pirates wear brightly colored garb with black and white strips and red scarves, no pirates have super powers unless cursed, and this is considered a non-self inflicted power.
P5 => It is against natural, self evident laws to be a pirate ninja or a ninja pirate or any other form of adjective, conjunction, noun, verb, modifier, expletive, infinitive or anything of the sort that implies directly or indirectly pirates are in some way also a ninja or that ninjas are in some way also pirates.
Q1 => All pirates are not ninjas.
Q2=> All ninjas are not pirates.
Thus, we can achieve the follwing Venn diagram.
______ __ ______
/ _____ \ / _____ \
| Ninjas | | Pirates |
\______/ \______/
I think we can all see that they do not in fact overlap.