Transcript Notes Section 2.

Geometry Notes
Section 2-2
What you’ll learn
How to determine truth values of
conjunctions and disjunctions
 How to construct truth tables

Vocabulary
Statement
 Premise
 Truth value
 negation
 Compound statement
 Conjunction
 Disjunction
 Truth table

Determining Truth Values



Statement—any sentence that is true or
false
 Usually denoted by p or q (the letter p
or the letter q represents the whole
statement)
Premise – just a simple statement
Truth Value—Two choices TRUE or FALSE
Examples:
 The carpet is red. FALSE
 Today is not Tuesday.FALSE
 All linear pairs of angles are
supplementary.
TRUE

Negations
Negation-the opposite of a statement
 Notation-- ~p
 Go back to the Examples:
 The carpet is red. FALSE
Negation:
 The carpet is not red. TRUE

Today is notTuesday. FALSE
 Negation:
 Today is Tuesday. TRUE

Determining Truth Values

One more example . . . .
All linear pairs of angles are
TRUE
supplementary.
 Negation: All linear pairs of angles are
not supplementary. FALSE


So if the original statement or premise
FALSE
is TRUE the negation will be ________.

So if the original statement or premise
is FALSE the negation will be
TRUE
________.
Conjunctions
 A compound
statement formed by
joining two or more simple statements
with the word AND.
 Symbolically—
Let
p represent a simple statement
Let q represent a second simple
statement
The conjunction is written as p Λ q
 Read
as “p and q”
Example
p represent “It is Tuesday.”
Let q represent “There is school
tomorrow.”
Let
The
conjunction is
It is Tuesday and there is school
tomorrow.
Truth Value of Conjunctions-- A conjunction
is only true when both simple statements are
true.
Let p represent “It is Tuesday.”
True or False? TRUE
Let q represent “There is school
tomorrow.”
True or False? TRUE
Therefore the conjunction
It is Tuesday and there is school
tomorrow.
TRUE
is _____________
disjunctions
 A compound
statement formed by
joining two or more simple statements
with the word OR.
 Symbolically—
Let
p represent a simple statement
Let q represent a second simple
statement
The disjunction is written as p ν q
 Read
as “p or q”
Example
p represent “It is Tuesday.”
Let r represent “It is snowing.”
The disjunction is
It is Tuesday or it is snowing.
Let
Truth Value of Disjunctions-- A disjunction is
true when only one simple statement is true.
Let p represent “It is Tuesday.”
True or False? TRUE
Let r represent “It is snowing.”
True or False? False
Therefore
the disjunction
It is Tuesday or it is snowing.
TRUE
is _____________
Conjunctions and Disjunctions can
be illustrated by. . . .

Venn Diagrams
The overlap is
the conjunction
p and q.
 The entire
shaded area is
p or q.

p
q
pΛq
Conjunctions and Disjunctions can be
illustrated by. . . .

Truth Tables
 You can compute the
truth value of a
conjunction or
disjunction using truth
tables.
 First consider all
possible truth value
combinations for p and
q (You will want to set
this up the same way
each time).
p
T
T
F
F
q
T
F
T
F
Conjunctions—”AND”
pΛq (BOTH MUST BE TRUE)

Take it one row at a
time
p
q
T
T
T
F
F
T
F
F
pΛq
p
q
~p
~q
~pΛ~q
Disjunctions—”OR”
p ν q (only has to be true)
p
q
T
T
T
F
F
T
F
F
pνq
p
q
r
~p
~r
qΛ~r ~pν(qΛ~r)
Have you learned?
How to determine truth values of
conjunctions and disjunctions?
 How to construct truth tables?
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
Assignment: Worksheet 2.2