Bob is a student but Carol is
not.
Sb & ~Sc
Everyone is
ambitious. (x)Ax
No one is working
hard. (x)~Wx
There are ambitious
students and there are
students
who do not work hard.
(Ex)(Sx
& Ax) & (Ex)(Sx & ~Wx)
Every student is
ambitious. (x)(Sx -> Ax)
Some students are not
working
hard. (Ex)(Sx & ~Wx)
If all students are
ambitious then Bob is
ambitious. (x)(Sx ->
Ax) -> Ab
Everyone who works
hard is
ambitious. (x)(Wx ->
Ax)
Only those who are
ambitious work
hard. (x)(Wx -> Ax)
Only those who work
hard are
ambitious. (x)(Ax ->
Wx)