Ex3:

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 not a disgrace. If he is not disgrace, then he is in the army. Therefore, he is in the army. (J,N,D,A)

2).If Algernon is a nuisance, then he is not in jail. If he is in jail, then he is a disgrace. If he 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).

3).Some foolish people drink whisky. Some students do not drink whisky. Therefore, some students are not foolish. (F(x), S(x), W(x))

4).Seniors only date juniors. Sam is a senior. Some dates Julie. Therefore, Julie is a junior. ((x),D(x,y),J(x))

5).Seniors who like mathematics do not date Elizabeth. Elizabeth only dates seniors. George date Elizabeth. Therefore, George does not like mathematics e