Using the letters indicated for propositions and variables, express the following using propositional logic and write the argument. If possible, find a derivation that shows that the argument is valid, indicate the rule of deduction used. Otherwise write CDNF(conclusion does not follow) -

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

2.) Seniors only date juniors. Sam is a Senior. Sam dates Julie. Therefore Julie is a junior.(S(x), D(x,y), J(x))

3.) Seniors who like mathematics do not date Elizabeth. Elizabeth only dates seniors.

4.)George dates Elizabeth. Therefore George does not like mathematics.