Summary
Implication(IF…THEN)
vacuously true -> true by virtue of the hypothesis
being false
| LHS: | RHS: | |||
|---|---|---|---|---|
| T | T | T | T | |
| T | F | F | F | |
| F | T | T | T | Vacuously True |
| F | F | T | T | Vacuously True |
Biconditional(IFF)
| LHS: | RHS: | ||||
|---|---|---|---|---|---|
| T | T | T | T | T | T |
| T | F | F | F | T | F |
| F | T | F | T | F | F |
| F | F | T | T | T | T |
Concept
Contrapositive
Converse
Inverse
Converse-inverse relationship, swapped terms from contrapositive
Arguments
-
Valid iff in every case where all the premises are true, the conclusion is true
-
Sound argument -> iff it’s valid and all its premises are true
-
Unsound argument -> may be valid, but it has a false premise
Syllogism -> an argument with 2 premises and a conclusion, ie. modus ponens and modus tollens
- Fundemental argument for most proofs
- Used in proof by contradiction
Other rules of inference
Application
Vacuously true, example
Proof for the contrapositive
Example for contrapositive, and converse and inverse errors
Negation of biconditonal