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Lecture 7

SSH 105 Lecture Notes - Lecture 7: Truth Table, Deductive Reasoning


Department
Social Sciences and Humanities
Course Code
SSH 105
Professor
Andrew Hunter
Lecture
7

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SSH Chapter 7
Symbo
l
Meaning Example
&Conjunction (and) p & q
Alice rode her bike, and John walked
VDisjunction (or) p V q
Either Alice rode her bike, or John walked
~Negation (not) ~ p
Alice did not ride her bike
Or
It is not the case that Alice rode her bike
Conditional (if-then) p q
If Alice rode her bike, then John walked
Conjunction (&)
- Two simple statements joined by a connective to form a compound statement
*True only if p and q are true
- Truth Table:
p q p & q
T T T
T F F
F T F
F F F
Disjunction (V)
- A compound statement of the form 'Either p or q'.
*True if either p or q is true. False if both are false.
- Truth Table:
p q p V q
T T T
T F T
F T T
F F F
Negation (~)
- The denial of a statement
*The reverse of the true/false statement
- Truth Table:
p ~ p
T F
F T
Conditional ( )
- If p then q
* False only when the antecedent is True and the consequent is False
- Truth Table:
P q p q
T T T
T F F
F T T
F F T
Tricky Arguments
- Example:
~ ( q & r ) It is not the case that both Leo and Jay sings the blues
~q & ~r Leo does not sing the blues, and Jay does not sing the blues
Prepositional Logic - The branch of deductive reasoning that deals with the logical relationship among statements
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