Chapter 3 section 1
A
statement
• Is a declarative sentence that is either true
or false. (using lower case letters p, q, r …)
• 2 Types of statement
 Simple – contains a single idea.
 Compound – contains several ideas.
 Determine
 1.
which sentence are statements.
More than half the households in the country
have digital cameras.
 2.
 3.
Come skiing with me this weekend in Tahoe.
You will be a millionaire by the time you are
30.
1.
Statement
2.
Not a statement
3.
statement
 AIDS
is a leading killer of men.
 Statement
 You’re
 Not
hired!
a statement
When
an idea is not true.
• Notation symbol is ~
• Example
 p:
The optical disk drive is included in the
price of the computer.
 Write
the sentence using negation.
 The optical disk drive is not included in the
price of the computer.
 Write the using symbolic notation.
 ~p
 Expresses
the idea of and.
• Symbol notation is

p
= the tenant pays utilities, d = $150
deposit is required
 Write
“It is not true that: the tenant pays
utilities and a $150 deposit is required”
symbolically.
I
can rewrite the statement as follows
~(p ^ d)
Write
the statement
•
~p ^ ~d
• The tenant does not pay utilities and does
not require a $150 deposit
•p^ d
 The tenant pays utilities and requires a
$150 deposit.
Conveys
the notion of or.
• Notation is V
Consider the following statements:
u: Urban sprawl will increase
c: Commuting will be more difficult
Write the statement symbolically
 Urban sprawl will not increase or commuting will be more
difficult.


(~u) V c
It is not true that: urban sprawl will increase or commuting will
be more difficult.
 ~(u
V c)
 Expresses
 Notation
the notation of if…then.

c represents “clean your room” and p represents
that you will be punished.
Write the following in symbolic notation
 If
you do not clean your room then you will be
punished.
 Solution
:
~c p
p = The Phillies win the world series
and s = Susan will win an Emmy.
 If
the Phillies do not win the world
series, then Susan will not win an Emmy.
~ p ~ s
 Represents
 Notation
the idea of if and only if.

p
= polygon has three sides
 t = it is a triangle.
 1.
A polygon has three sides iff it is a
triangle.
s
= the software can be returned
 b = the seal is broken
 2.
The software can be returned iff the seal
is not broken
1. p  t
2.s ~ b
 r = The republicans will control congress
 t = taxes will be cut
 s= social programs will be increased
 1)
The republicans will control congress or
social programs will not be increased.
 2)
The republicans will not control congress and
the social programs will increase.
 3)
If social programs are not increased, then the
republicans will not control congress or taxes
will not be cut.
1.r  ~ s
2. ~ r  s
3. ~ s  ~ ( r  t )
 t=
radial tires are included
 s= sunroof is extra
 w= power windows are optional
 1.
It is not true that the sunroof is extra and
the redial tires are included.
 2.
If the sunroof is extra and the radial tires
are included, then the power windows are
not operational.
1. ~ ( s  t )
2.( s  t ) ~ w
 Identify
each statement as simple or
compound if the statement is compound,
identify the connectives uesd.
 1.
4. Alvaro likes opera.
 2. LeBron or Kobe will lead the conference
in scoring.
 3. If you want to ride, you must be at
least 48 inches tall and have no food,
drinks, or Kryptonite.
 1.
Simple
 2.
Compound; or
 3.
Compound; if…then, and, or
 1.
Global warming will increase if and
only if we do not develop alternative
energy source.
 2.
If global warming does not increase
then; Congress will not pass new energy
legislation and we will not develop
alternative energy source.
1. g  ~ a
2.(~ g )  (~ c  ~ a)
Thanks