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Chapter 1.1

# COSI 29a Chapter Notes - Chapter 1.1: Exclusive Or, Contraposition, Logical Biconditional

Department
Computer Science
Course Code
COSI 29a
Professor
Cherniack Mitch
Chapter
1.1

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Logic
Pages 1 20
Propositions
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).
Implications
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
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