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)