Which of the following arguments (i.e. logical calculations) reach logically valid conclusions, and which do not? Which argument utilizes the logical rule of modus ponens?

A. If Fred got an A in the course, then he must have done all the work. Freddid get an A in the course, so therefore he didn’t do all the work.

B. If Fred got an A in the course, then he must have done all the work. Fred did get an A in the course, so therefore he must have done all the work.

C. If Fred got an A in the course, then he must have done all the work. Fred did do all the work in the course, so therefore he did get an A.

D. If Fred got an A in the course, then he must not have done all the work. Fred didn’t get an A in the course, so therefore he must not have done all the work.