Propositional Logic Functions
Read these four sections to learn how to identify and apply propositional (or sentential) logic functions. Using these symbols, you should be able to turn statements into symbolic formulas to more clearly see the logical connections taking place and determine when the conclusions are valid. It can look confusing at first, but moving slowly through these units will allow you to make valid logical proofs.
As you go, complete the exercises, then check your answers against the answer keys.
Note that the symbols used in some places can differ slightly from those used elsewhere. This is because there is not one standard set of symbols used for sentential logic, but a few. This table shows you the differences and helps translate between them.
In the resources in this course, the symbols for disjunction and negation are the same in both systems, but the symbols for conjunction, conditional, and biconditional are different.
| Name | Meaning | Symbol 1 | Symbol 2 |
| Conjunction | and | & | • |
| Disjunction | or | v | v |
| Negation | not | ~ | ~ |
| Conditional | if/then | → | ⊃ |
| Biconditional | if and only if | ↔ | ≡ |
Exercise
Answers
- Not truth functional.
- Truth functional: Tom is a fireman. Tom is a father.
- Not truth functional.
- Not truth functional.
- Truth functional: Cameron Dias has had several relationships. Cameron
Dias has never married. - Not truth functional.
- Not truth functional.
- Not truth functional.
- Truth functional: Jack is a cowboy. Jill is a cowboy.
- Truth functional: Josiah is Amish. Josiah is a drug dealer.
- Truth functional: The Tigers are the best baseball team in the state. The Tigers are not as good as the Yankees.
- Truth functional: Bob went to the beach to enjoy some rest. Bob went to the beach to enjoy some relaxation.
- Truth functional: Lauren isn't the fastest runner on the team. Lauren is fast enough to have made it to the national championship.
- Truth functional: The ring is beautiful. The ring is expensive.
- Truth functional: It is sad that many Americans to not know where their next meal will come from. It is true that many Americans do not know where their next meal will come from.