~B ~B--> (G-->F) (A-->E) B v (A v G) E v F How would I go about answering this problem with putting in inference rules to the proof?

We establish or infer the truth of a proposition by the
truth tables.

~B is the negation of  proposition
B.

When B is true (T), ~B is not true. When B is false( F)
, ~B is True (T).

Truth or inference table for 
~B--> (G-->F) . Please do not get confusion for proposition in heading
and  the false value, F in the ttruth table:

 ~B   G     F  
 (G-->F)          ~B-->
(G-->F)

   T    T     T       
T                        T

   T    T      F      
F                         F

   T    F      T       
T                       T

   T   
F      F        T                        T

   F     T    
T        T                        T

   F     T     
F       F                        T

   F    F       T     
T                         T

Truth table for
(A->E)

 A      E          
(A->E)

T       T             
T

T      
F              F

F       T              T

F      F               T

 F     F             
T                        

Truth or inference  table for  B
v (A v G).

B     A       G         (AVG)          
BV((AVG)

T     T        T             T                  
T

T     T        F             T                   
T

T      F       T             T                   
T

T     
F       F             F                    T

F     
T        T            T                    T

F      
T       F            T                   
T

F       F      T             T                   
T

F       F      F             F                    F  

The
truth table  for (EVF) . There proposition F in the heading and in the truth infering
table  the false value F. Please do not get confused about the different
F's.:

E         F            (E V
F)

T         T                  T

T         
F                 F

F         
T                 T

F         
F                 T