Truth Table for Propositions
Each row of a proposition p's truth table represents how things would stand with p for a
single possible combination of truth of its components simple statements. SO the n
Rules of Implication
Where the truth tables fail
Truth tables do not work for quantitative statements.
They actually only work nicely for propositional logic.
They also fail at practicality (10 sim
Rules of Replacement
p:q p is logically equivalent to q
First Five Rules of Replacement
DeMorgan's Rules (DM)
o ~(p.q):(~pv~q)
o ~(pvq):(~p.~q)
Commutativity (Com)
o (pvq):(qvp)
o (p.q):(q.p)
Assoc
Symbolic Meaning
Simple Statement (atomic statements)
A statement that contains no other statement as a part (component, constituent).
Snow is white.
My hovercraft is full of eels.
Upper case letters
Valid and Invalid Statements
Ex. of proving a statement of being deductively valid
All humans are mortal
Barack Obama is a human.
Barack Obama is mortal. (T/T)
Deductive validity states that it is imp
FormsandValidity
ArgumentForms:patternofreasoning
ModusPonens:modeorwayofpositing
IfA,thenB
A
SoB
A,Barevariablesthatstandforstatements
Substitutioninstance:uniformlyreplacevariablesinthatformwithstat
Logic Concepts
Basic concepts
Logic is the study of methods for evaluating whether the premise of an argument
support its conclusion
Argument set of statements where some of the statements are intende
Modus Ponens: valid argument form
If A, then B
A, so B
Any substitution instance of the variables will result in a valid argument as
long as?
Conditional statements: if-then
If is the ?
then is the ?