Truth Tables
Remind students of the basic truth tables:
Transformation Rules
Simplification
and 
Addition
and 
Modus Ponens
Modus Tollens
Hypothetical Syllogism
Disjunctive Syllogism
and 
Conjunction
Constructive Dilemma
Problems
If it is raining or snowing, I've got my umbrella. It is raining. Therefore I have my umbrella.
First: Make it symbolic, where p is "it's raining" and q is "it's snowing" and r is "I have my umbrella."
(This is given: If (it's raining or it's snowing) then (I will have my umbrella).)
(This is also given: It is raining.)
(We have from step 2, and we
can use the Addition rule to get us .)
(We have from step 3, and
from step 1, and we can use Modus Ponens to arrive at ,
which is what we're looking to prove.
I am wearing a shirt and a pair of pants. I am wearing shoes. Therefore I am wearing a pair of pants and shoes.
shirt and pants -> pants. pants + shoes.
If I pass the quiz, I will pass the class. I did study. If I study I will pass the quiz. Therefore I will pass the class.
quiz -> class. study. study -> quiz. two ways to do it. hypothetical syllogism or two modus ponens.
If she's pregnant, I will marry her. On the other hand, if she's not pregnant I am going out with my friends to the movies. I'm not marrying her. So off the movies I go!
pregnant -> marry. not-pregnant -> movies. pregnant or not-pregnant, then use a disjunctive syllogism.
Either I am wearing slacks or I am wearing a dress. I'm not wearing a dress. Therefore I'm either wearing slacks or a kilt.
Replacement Rules
Double Negation
Implication
Transposition
Commutation
and 
Distribution
and 
Association
and 
Biconditionalization
DeMorganization
and 
Exportation
Repetition
and 
Assumption Rules
Deduction
Reductio ad Absurdum
