Agenda
<aside> 📌 Reminders
<aside> 💡
A truth table shows all possible truth values for logical expressions based on combinations of truth values of their components.
</aside>
For example, consider the logical expression P ∧ Q (P AND Q):
| P | Q | P ∧ Q |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |
<aside> 💡
An argument is valid if the conclusion logically follows from the premises. To check validity, we can use a truth table:
Example:
P → QPQTruth table for validity check:
| P | Q | P → Q | P | Q (Conclusion) |
|---|---|---|---|---|
| T | T | T | T | T |
| T | F | F | T | F |
In this case, the argument is valid when both premises are true.
<aside> 💡
Two logical statements are logically equivalent if their truth tables yield the same result for all truth value combinations.
</aside>
Example:
¬(P ∨ Q) (NOT (P OR Q))¬P ∧ ¬Q (NOT P AND NOT Q)| P | Q | ¬(P ∨ Q) | ¬P | ¬Q | ¬P ∧ ¬Q |
|---|---|---|---|---|---|
| T | T | F | F | F | F |
| T | F | F | F | T | F |
| F | T | F | T | F | F |
| F | F | T | T | T | T |