This lecture explains how to string multiple logical expressions together.
Takeaway Points
- We can combine logical operators in an intuitive manner. For instance, P v ~ Q means that P or not Q is true (or both).
- Operators can only work on one expression at a time. For example, P v Q v R does not work. (P v Q) v R or P v (Q v R) does.
- Our logical operators can work on compound sentences just as they do for simple sentences. For example, you could negation a disjunction like this: ~(P v Q).
- Compound sentences are much harder to translate from English to logic than simple simple sentences. Be careful to capture the intended meaning; ask the speaker if you are unsure.
- An English expression will sometimes have multiple translations into logic, but logic will only have one (non-trivial) translation back to English. This is one reason why logic is so useful!
- To be a clearer writer, make sure you avoid using English sentences that can be translated in more than one way.