GeomP1 15.1 ­ Logic and Truth Tables
September 19, 2016
Four Types of Statements
Conditional: If p, then q.
Assuming the conditional is True, which of the others are True and which are False (not always True)?
Converse: If q, then p.
Inverse: If ~p, then ~q.
Contrapositive: If ~q, then ~p.
Every even year, the Giants win the World Series.
Conditional: If it's an even year, then the Giants win the World Series.
Converse: If the Giants win the World Series, then it's an even year.
Inverse: If it's not an even year, then the Giants don't win the World Series.
Contrapositive: If the Giants don't win the World Series, then it's not an even year.
Logic ­ Building and Evaluating Arguments
A statement is a sentence that is either true or false. The truth value of a statement is whether it is true or false. We simplify statements by replacing them with variables.
By adding "not" to a statement, it is negated, using the symbol ~.
M: Menlo Park is the capital of California. T
F
~M: Menlo Park is not the capital of California. T
F
GeomP1 15.1 ­ Logic and Truth Tables
September 19, 2016
Truth Tables
If a statement is true, then its negation is false.
If a statement is false, then its negation is true.
This can be represented with a truth table.
S
~S
S: My dog's name is Sophie.
T
F
~S: My dog's name is not Sophie.
F
T
Conjuctions and Disjunctions
Two statements can be joined to create a compound statement. J: I play jazz piano R: I listen to rock music.
Joining with and is a conjunction and uses the symbol ^:
J ^ R: I play jazz piano and I listen to rock music.
True only when both statements are true.
GeomP1 15.1 ­ Logic and Truth Tables
September 19, 2016
Conjuctions and Disjunctions
Two statements can be joined to create a compound statement. J: I play jazz piano R: I listen to rock music.
^
Joining with or is a disjunction and uses the symbol :
^
J R: I play jazz piano or I listen to rock music.
True if either statement is true (or if both are true).
Truth Tables and Compound Statements
p: I like parties
q: I like quiet time
Conjunction
Disjunction
p
q
p^q
p
q
p^q
T
T
T
T
T
T
T
F
F
T
F
T
F
T
F
F
T
T
F
F
F
F
F
F
GeomP1 15.1 ­ Logic and Truth Tables
Conditional Statements and Truth Tables
If I am hungry, then I will eat an apple.
Conditional Statements and Truth Tables
If I am not hungry, then I will not eat an apple.
September 19, 2016