1.  Conjunctive Normal Form: A logic form must satisfy one of the following conditions 1) It must be a single variable (A) 2) It must be the negation of a single variable (~A) 3) It must be the disjunction of 2 or more terms. (~C  B  A) 4) It must be a conjunction of any of the 3 conditions above. (~A  B)  (C) Conjunction of Disjunctions

2.  Disjunctive Normal Form: A logic form must satisfy one of the following conditions: 1) It must be a single variable (A) 2) It must be the negation of a single variable (~A) 3) It is a conjunction of 2 or more terms (~C  B  A) 4) It is a disjunction of two or more terms each of which is one of the 3 types above. (~C  B)  (D  A) disjunction of conjunctions

4.  A tautology is a logic form that always has truth value TRUE.  A contradiction is a logic form that always has truth value FALSE.  A contingency is a logic form that is sometimes true and sometimes false.

5. Ex 1: Z: a  (b  a)

8.  A logic form is a tautology if and only if it can be reduced to merely a variable symbol and the disjunction of its negation. (a  ~a)  Tautology A  B  D  ~B  Not a tautology A  B  ~D ; (~A  B)  (B  ~B)

9.  Z: a  (b  a)

10.  A disjunctive normal form is a contradiction if and only if it can be reduced to the conjunction of a variable and its negation. (D  ~D)  Contradiction: (~C  C  A)  Not a Contradiction: (~C  C)  (C  A)

11.  Ex 3: Y: ~[(~b  a)  a]  a