Chapter 2 - Logic

Biconditional

P <=> Q is the conjunction of the implication P => Q and its converse - (P => Q) ∧ (Q => P) - P if and only if Q

Implication Parts

P => Q means P implies Q (If P, then Q) and P is called the premise/hypothesis and Q is called the conclusion

Distributive Laws

P ∨ (Q ∧ R) ≡ (P ∨ Q)∧(Q ∨ R) same thing if you switch every symbol

Conjunction

The conjunction of the statements P and Q is the statement: "P and Q" denoted by P ∧ Q

Disjunction

The disjunction of the statements P and Q is the statement "P or Q" and is denoted by P ∨ Q

Negation of a statement

The negation of the statement P is called not P and is denoted by ~P

Tautology

a compound statement S is called a tautology if it is true for all possible combinations of truth values of the component statements that comprise S - basically if it is always true

Contradiction

a compound statement is a contradiction if it is false for all possible combinations of truth values

Logically equivalent

denoted by R≡S - Let R and S be two compound statements including the same component statements - if they both have the same truth values for all combinations of truth values of their component statements

Converse

the converse of P => Q is Q => P

Exclusive or

when either condition may be true, but NOT both

De Morgan's Laws

~(P ∧ Q) ≡ (~P)∨(~Q) ~(P ∨ Q) ≡ (~P)∧(~Q)