Chapter 8 Logic Topics 3.1-3.4

Propositions Must be objective (fact-based) Cannot be a question May be indeterminate (the statement does not have the same answer for all people)

Pg. 233 example 1

Proposition notation Represented by letters such as p, q, & r. The negation of a proposition is “not p”, and is written as ¬p. The truth value of ¬p is the opposite of the truth value of p.

Pg. 234 Example 2

Negation & Venn Diagrams U: Universal set P : Truth set P’: ¬p

Pg. 235 Example 3

Compound Propositions Connective Symbol conjunction and True only when both propositions are true disjunction or True when one or both propositions are true exclusive disjunction or, but not both True when only one proposition is true

Truth tables

Pg. 241 example 5

Tautology, Logical Contradiction & Logical Equivalence

Pg. 241-244 examples 6-9 6.

7.

8.

9.

Implication & Equivalence Implication: When 2 propositions can be linked with “If... then….” p is the antecedent; q is the consequent Equivalence: When 2 propositions can be linked with “…if and only if…” Statement Symbol If p then q Statement Symbol p if and only if q

Implication & Equivalence Truth Tables Pg. 247 #5

Pg. 247 #6

Converse, Inverse & Contrapositive

PG. 248 #1

PG. 248 #2

VALID ARGUMENTS A tautology indicates a valid argument.