Communitive Law
A^B is equivalent to B^A
Associative Law
A^(B^C) is equivalent to (A^B)^C
Distributive Law
A^(B^C) is equivalent to (A^B)^(A^C)
Identity Equivalence
A^T=A && AorF=A
Complementation Law
AorA’=T && A^A’=F
DeMorgan’s Law
(A^B)’ = A’orB’
Double Negation
A’’ = A
Equivalence
(A implies B) ^ (B implies A)
Implication Rule
A implies B == A’orB
Modus Ponens
Given A, have A implies B, conclude B
Modus Tollens
Given A implies B and B’, conclude A’
Conjunction
Given A and B, conclude A^B
Simplification
Given A^B, conclude A or B
Addition
Given A, conclude AorB
Hypothetical Syllogism
Given A implies B and B implies C, conclude A implies C
Self
Given AorA, conclude A
Deduction
Can pull out first term of an implies and add it with an and to the hypothesis
Contrapositive
A implies B == B’ implies A’
Universal Instantiation
(Ax)Px == Pt for a variable
Existential Instantiation
(Ex)Px == Pa, where a is constant
Universal Generalization
Px == (Ax)Px, no free variables
Existential Generalization
Px or Pa == (Ex)Px, x must not appear before equals
Neg Rule
[(Ex)Ax]’ == (Ax)[Ax]’
Proof by exhaustion
Check every possible case, must have only a specific number of cases
