Story driven logic problem.

Hi everyone,

Just started my computer science studies and don't have any advanced foundations in math (studied litterature in school).

I'm faced with a story driven logical problem which i've translated into the following equasions.

1. if A false and B true => C is False
   
2. if D true => A is true
   
3. if E true and A true => B is true
   
4. if I true => E false or D false
   
5. if E true and I false => D false and A false
   
6. if E false => F true and B false
   
7. if C true => H false
   
8. if D false and C true => I true
   

I then need to answer if E is true, if D is true , if I is true , (...) if when C true => A true? if when C false => A false? (blah blah blah)

Anyways, i'm not asking for a fed out solution, I've actually found all the answers by using a table I designed (E and D must be false.. from there on, it's a piece of cake). But my method is for the least... barbaric, and doesn't prove anything to correctors, without some written formulas.

Could someone give me some more "academic" methods? We've been studying arrays/groups (Mengen?), functions, relations and so on...

*Being French in a German seminar doesn't help understanding.*

Thanks !