MATH 302 Lecture 3
Jump to navigation
Jump to search
« previous | Monday, September 3, 2011 | next »
Tentative homework session Thursdays 7-8pm in BLOC 117
Propositional Logic
a declarative sentence which is either true or false.
Exampes:
- Tomorrow it will rain.
- 1 + 3 = 5
- This sentence is false.
Logical Connectives
(See Propositional Logic#Logical Connectives→)
Creates a compound proposition
| p | q | conditional p → q |
converse q → p |
inverse ¬p → ¬q |
contrapositive ¬q → ¬p |
(negation) ¬(p → q) |
(negation eq) p ∧ ¬q |
|---|---|---|---|---|---|---|---|
| T | T | T | T | T | T | F | F |
| T | F | F | T | T | F | T | T |
| F | T | T | F | F | T | F | F |
| F | F | T | T | T | T | F | F |
Therefore, the negation of "if, then" is "and, not"
Special Propositions
- tautology
- always true regardless of input
- p ∨ ¬p
- contradiction
- always false regardless of input
- p ∧ ¬p
- contingency
- neither a tautology or a contradiction
Logical Equivalence
(See Propositional Logic#Logical Equivalence→)
Two propositions are equivalent iff they have the same truth tables.