I’ve had some students request a few more rules of thumb for recognizing what kinds of noncategorical propositions are represented by different constructions in English. It is important to keep in mind that these are only rules of thumb, and that there are occasional exceptions. You will have to think through every case individually. But these rules of thumb are often true:
Conjunction
And and but usually indicate conjunction. For instance,
I went to the store and I did not buy anything.
I went to the store but I did not buy anything.
Disjunction
Or often indicates disjunction (but not always). For instance:
I went to the store or I went home.
Either…or also usually indicates disjunction, although sometimes it indicates both a disjunction and conjunction. For instance:
Either I went to the store or I went home
is a disjunction if it is possible for both to be true. If it is not possible for both to be true it’s really an abbreviation for:
Either I went to the store and did not go home or I went home and did not go to the store.
This uses both conjunction and disjunction.
Conditional
If is the most common word indicating a conditional. For instance,
If I go to the store, I will buy milk.
Only if is also a common indicator. For instance:
Tom likes Mary only if Mary is smart.
You have to be careful about if and only if, because they are in a sense the reverse of each other. The following sentences do not represent the same conditional:
Tom is tall if Mary is short.
Tom is tall only if Mary is short.
The first says that if it is true that Mary is short, Tom has to be tall. The second says that if it is true that Tom is tall, Mary has to be short.