MATH 135
Fall 2008
Lecture III Notes
Notation
Some notation to remember:
Z
=
{
. . .

3
,

2
,

1
,
0
,
1
,
2
,
3
, . . .
}
= set of integers
P
=
{
1
,
2
,
3
,
4
, . . .
}
= set of positive integers
N.B. This notation is not standard, but is used by our textbook.
R
= the set of all real numbers
Compound Statements
If
A
and
B
are mathematical statements, we often see compound statements such as “
A
and
B
” and
“
A
or
B
”.
We deﬁne what the words “and” and “or” mean mathematically by using an organizational chart
called a truth table:
A
B
A
and
B
A
or
B
T
T
T
T
T
F
F
T
F
T
F
T
F
F
F
F
A
truth table
lists all possible combinations of TRUE (T) and FALSE (F) for the original statements
and tells us whether the compound statement is TRUE or FALSE in each case. (Truth tables can
be used to look at more complex compound statements, but we won’t do this in MATH 135.)
From the table, for “
A
and
B
” to be TRUE, both
A
and
B
must be TRUE.
Otherwise (when one is FALSE or both are FALSE), “
A
and
B
” is FALSE.
For “
A
or
B
” to be TRUE, either or both of
A
and
B
must be TRUE.
Otherwise (when both are FALSE), “
A
or
B
” is FALSE.
This makes sense when we consider the normal English language usage of these words.
Example
A
=“2 is a prime number”,
B
=“5 is a perfect square”
Is “
A
and
B
” TRUE or FALSE?
Is “
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 Fall '08
 ANDREWCHILDS
 Algebra, Integers, Natural number, Prime number

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