Keep in mind always the general rule: universal quantifers are linked with implications, existential quantifiers with conjunctions.
Suppose we want to say that any good student in the course will do most of the exercises. Alice is a good student. Should it not follow that she will do at least some of the exercises? Careful: we have not yet specifically indicated that she is in the course. Let's do that, and see the argument form that would result.
(we'll use Gx for "good student,"
Cx for "being in the course," Ey
for "exercise," and Dxy for "x does y")
Ax((Gx & Cx) -> Ey(Ey & Dxy)), Ga
& Ca |- Ey(Ey & Day)
Even apart from the need to remember that on these pages we are using A's and E's outside the parentheses as quantifiers and not as variables, we need to note that the difference between "most" and "at least some" has been lost.
For our drill, symbolize the following cases.
1. Most honor students are ambitious,
and everyone ambitious takes some difficult courses. Anyone taking
difficult courses works hard. Therefore, there are honor students
who work hard.
2. No honor students are lazy.
Anyone not lazy takes difficult courses. It's necessary for someone
taking difficult courses to work hard. Therefore, there are students
who are working hard.
3. Only honor students take difficult
courses. None of the courses that the men are taking are difficult.
Therefore, only women are honor students.
4. Anyone not an honor student takes
all easy courses. Alice is taking courses that are not easy.
Therefore, Alice is an honor student.
Do you think all of these are valid arguments? Do you
think any of them are?
After you have done these on your own, click
here and compare your symbolization with mine.