Putting it Together in QL
 

Back in Chapter 7, we showed that our truth-functional operators from PL can be employed in their usual way in QL, namely to connect wffs. This is no less true now that we have categorical propositions at our disposal. We can combine any wffs from QL in any way we like using our PL operators.   Let's look at some examples.

What's the main operator? Clearly this is a conjunction. The left conjunct is a categorical proposition of the E variety.

The right conjunct is a bit trickier. Ignat isn't a skier, but is he a philosopher who doesn't ski or just any old person who doesn't ski? The sentence doesn't make the answer to this question explicit, but the natural interpretation is that Ignat is a philosopher. So the right conjunct is a conjunction of a singular proposition and  the negation of the singular proposition. (remember those?)

So the whole conjunction is:

This is but one example. Again, we can put wffs of QL together in any combination. The following exercises will give you ample practice.

Recognizing and Rewriting Categorical Propositions
Monadic Predicate Logic Translation
Mixed Translation Exercise
Yet More Translation