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A portion of the course materials for csce 235, fall 2008, focusing on propositional logic. It covers defining propositions, connectives, truth tables, precedence of logical operators, and their use in various fields such as bitwise operations, theoretical computer science (sat), and programming. The document also includes exercises on propositions, truth values, conditional statements, and logical equivalences.
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Logic CSCE 235, Fall 2008
Defining Propositional Logic - Propositions - Connectives - Truth tables - Precedence of Logical Operators - Usefulness of Logic - Bitwise operations - Logic in Theoretical Computer Science (SAT) - Logic in Programming - Logical Equivalences - Terminology - Truth tables - Equivalence rules
Logic 235, Fall 2008
Logic 235, Fall 2008 Exercise1.1:
c)
(yes.
d)
(yes.
e) x+
(No.)
f) Answer this question. (No.)
Logic 235, Fall 2008 Exercise1.1:
If
then
If
then
If
then
If monkeys can fly, then
Logic 235, Fall 2008 Exercise1.1: Construct a truth table for each of these compound propositions.
a) p ∧ ¬ q^ p q p ∧ ¬ q
Logic 235, Fall 2008 Exercise1.1: Construct a truth table for each of these compound propositions.
a) p ∧ ¬ q^ p q p ∧ ¬ q 0 1 0 1 0 0
Logic 235, Fall 2008 Exercise1.1: Construct a truth table for each of these compound propositions.
c) (p ∨ ¬ q ) → q p q ¬ q p ∨ ¬ q (p ∨ ¬ q) → q 1 1 0 1 1 1 0 1 1 0 0 1 0 0 1 0 0 1 1 0
Logic 235, Fall 2008
a) p
q
q
p^ p q p ∨ q q ∨ p 0 0 0 0 0 1 1 1 1 0 1 1 1 1 1 1 The two columns in the truth table are identical, thus we conclude that p ∨ q ≡ q ∨ p
