Chapter 1.1 Outline
Pages 1 – 20
A declarative sentence that is either true or false.
The negation of a proposition (p) is denoted by ¬p (aka “not p”).
Ex: The negation of “Today is Friday” is “Today is not Friday”.
p ∧ q is called the conjunction of p and q.
p ∨ q (“p or q”) is called the disjunction of p and q.
The exclusive disjunction of p and q is denoted p ⨁ q (either p or q is true but not both).
The implication p → q (if p, then q) is only false when p is true and q is false (if the condition p
is met then q must be also met).
Ex: “If you get 100%, then you will get an A.” This statement is only false if you get 100% (p)
but you do not get an A (q).
The proposition q → p is the converse of p → q.
The proposition ¬p → ¬q is the inverse of p → q.
The proposition ¬q → ¬p is the contrapositive of p → q. The contrapositive has the same truth
value as p → q. Since they have the same truth value they are called equivalent.
The converse and inverse are equivalent.
The biconditional p ↔ q is true when both p and q have the same truth values. p ↔ q is
equivalent to (p → q) ∧ (q → p).
Precedence of Logical Operators Negation has precedence over conjunction, conjunction has precedence over