A. Using the following translation scheme, translate the following into the language of predicate logic:

U: People [This is the universe of discourse, not a predicate]
Fx: x fails all of his or her classes
Jx: x is a junior.
Lx: x studies logic.
Sx: x is a student.
Wx: x works hard.
a: Alonzo
g: Gottlob

1. Alonzo works hard.

2. If Alonzo is a student, the Gottlob either studies logic or is a junior.

3. No one studies logic.

4. Not everyone who studies logic works hard.

5. At least one junior studies logic, but not every junior does.

6. Every student who studies logic works hard but does not fail all his or her classes.

7. The only students who fail all their classes are those who either take logic or do not work hard.

8. Any student who studies logic will fail all his or her classes if no one works hard.

B.Translate the following into smooth, accurate, and idiomatic English, using the same abbreviation scheme above:

9. ∃x[Sx& (Lx∨Wx)]

10. ∀x[(Sx& Lx)→(∃yWy→Wx)]