A very brief description of basic logical connectives and quantifiers.

1. Shannon O’Neill: Homework 1 due September 4th 2014

2. Statements are
true or false but
NOT both
Statements used in
this presentation
will be
P
I mowed the lawn
Q
I got paid

3. Conjunctions
P. Q. P^Q
T T T
T F F
F T F
F F F
P^Q
“I mowed the lawn
AND I got paid.”

4. Disjunctions
P Q PVQ
T T T
T F T
F T T
F F F
PVQ
“I mowed the lawn
OR I got paid.”

5. Implications
P. Q. 퐏 퐐
T T T
T F F
F T T
F F T
푷 푸
“IF I mow the lawn
THEN I get paid.”

6. Quantifiers
Symbols used to give the value of a variable within a given set
Universal
“FOR ALL x in the
Natural numbers x is less
than x+1”
∀푥휖푁: 푥 < 푥 + 1
Existential
“THERE EXSITS an x in
the Natural number that
is prime”
∃푥휖푁: 푥 푖푠 푝푟푖푚푒

7. Review
Logical connectives turn
statements into propositions.
Conjunctions (AND) are
only true when all the
statements are true.
Disjunctions (OR) are
only false when all
statements are false.
Implications (IF...THEN)
are only false when the
condition is true and the
antecedent is false.
Quantifiers describe the
value of a variable in a given
set.
Universal quantifiers
mean that ANY element
in the set satisfies the
given conditions.
Existential quantifiers
mean that AT LEAST
ONE element in the set
satisfies the given
conditions.

8. Sources
• Blackboard
• Basic Color Theory from Colormatters.com
• PowerPoint: Presentation Tips from Bates.edu
• Presentation Design Tips from Reynolds
• Additional Sources
• http://www.sc.edu/cte/guide/powerpoint/