The translations

Key

P Fry eats Bachelor Chow.
Q Bender eats Bachelor Chow.
R Fry will drink Slurm.
Translations and proofs.

6. Either the Professor Plum or Miss Scarlet killed Colonel Mustard. If Professor Plum killed Colonel Mustard, then Professor Plum was in the kitchen. If Miss Scarlet killed Colonel Mustard, then she was in the drawing room. If Miss Scarlet was in the drawing room, then she was wearing boots. But Miss Scarlet was not wearing boots. So, Professor Plum killed the Colonel.

Key

P Professor Plum killed Colonel Mustard.
Q Miss Scarlet killed Colonel Mustard.
R Professor Plum was in the kitchen.
S Miss Scarlet was in the drawing room.
T Miss Scarlet was wearing boots.
(P v Q)
(P --> R)
(Q --> S)
(S --> T)
¬T
_____
P


7. Either Mrs. White or Mrs. Peacock stole the diamonds. If Mrs. Peacock stole the diamonds, then she was in the billiards room. But if Mrs. Peacock was in the library, then she was not in the billiards room. Therefore, if Mrs. Peacock was in the library, Mrs. White stole the diamond.
Key

P Mrs. White stole the diamonds.
Q Mrs. Peacock stole the diamonds.
R Mrs. Peacock was in the billiards room.
S Mrs. Peacock was in the library.
(P v Q)
(Q --> R)
(S --> ¬R)
_____
(S --> P)