ercise 3: For the following argument, try to construct sentential derivations. In some cases, the argument is invalid, in which case write 'CDNF" (conclusion does not follow), use the letter indicated: 1. If Algernon is in jail, then he is not a nuisance to his family. If he is not in jail, then he is 2. If Algernon is a nuisance, then he is not in jail. If he is in jail, then he is a disgrace. If he 3. Some foolish people drink whiskey. Some students do not drink whiskey. Therefore some 4. Seniors only date juniors. Sam is a Senior. Sam dates Julie. Therefore Julie is a 5. Seniors who like mathematics do not date Elizabeth. Elizabeth only dates seniors. George not a disgrace. If he is not a disgrace, then he is in the army. Therefore he is in the army.(J, N, D, A) is a disgrace, then he is not in the army. Therefore, he is either not in the army or not a nuisance(J,N,D,A). students are not foolish.(F(x), S(x), W(x)) junior. (S(x), D(x,y), J(x) dates Elizabeth. Therefore George does not like mathematics