Logical Equivalence - kenhendricks00/DiscreteMathematics GitHub Wiki
Definition P ≡ Q
Propositions P and Q are logically equivalent if they produce the same truth value
Example
Show that p → q is logically equivalent to ¬p V q
| p | q | ¬p | p → q | ¬p V q |
|---|---|---|---|---|
| T | T | F | T | T |
| T | F | F | F | F |
| F | T | T | T | T |
| F | F | T | T | T |
Propositions p → q and ¬p V q produce the same truth values!
∴ p → q ≡ ¬p V q
Useful laws for logical equivalence
Examples
Simplify the compound propositions with above laws and produce the truth value if possible
