I.
Unit One
A. Logical Operators
1. Negation, “not”, ~, opposite value of original proposition
2. Conjunction, “and”, , only true if both sides are true
3. Disjunction, “or”, v, only false if both sides are false
4. Conditional, “If…then”, Ɔ, only false when the first is true and the second is false
5. Biconditional, “if and only if”, ≡, true when both sides have the same truth vale
B. Truth Tables
1. General
a. Number of Rows determined by 2^Number of Variables
b. First variable: 1st 1/2 of rows “T”,
c. Each subsequent variable alternates twice as frequently
2. Validity
a. Complete the Table
b. If a row exists in which the premises are true, but the conclusion is false it is invalid
3. Logical Equivalence
a. Place a biconditional between two propositions
b. Complete the table
c. If the biconditional is true on every row, logically equivalent
C. Shorter Truth Table Method
1. Validity
a. Assume invalid by assigning the premises T and the conclusion F
b. Complete row
1) If no forced truth values
a) Assume truth value for one variable
b) If contradiction, assume opposite value
2) No contradiction=Invalid
2. Consistency
a. Assume all propositions are True (T under each)
b. Complete—No contradiction=Consistent
3. Logical Equivalence
a. Assume not LE by assigning opposite truth values (One T and one F)
b. Complete Row
1) No contradiction—not LE
2) Contradition
a) Switch assumed truth values
b) No contradiction—not LE
D. Dilemma 
1. Go between the horns
a. Deny the 2nd (disjunctive) premise
b. Provide a 3rd option
2. Grasp it by the horns
a. Reject one of the conditionals in the 1st (conjunctive) premise
b. If either conjunct is false, the whole conjunction is false
3. Rebut the horns
a. Use a Counter Dilemma
1) Same components
2) Not necessarily same form as original
b. Most rhetorically effective