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View Full Document Predicates and Variables
A
predicate
is a statement that becomes a proposition when we
substitute values for all
variables
.
Examples
:
“
x
2
<
10”
or
“My current grade in course
x
is
y
”
We use the notation
P
(
x
)
to denote predicate
P
with variable
x
—
Q
(
x
,
y
)
denotes a predicate with two variables
Given a predicate
P
(
x
), we can ask two kinds of questions:
— Is there a value for variable
x
for which
P
(
x
) is true?
— Is
P
(
x
) true for all possible values of
x
?
In both cases, an important point will be: what possible values can
x
take?
Existential Quantifier (
∃
)
Consider: “There is some rational number whose square is 2.25”
In symbols, we say:
∃
x
∈
Q
,
x
2
= 2.25
— there exists a rational number
x
such that
x
2
= 2.25
— there exists
at least
one such rational number (actually two)
— If we want to say “there exists exactly one
x
…” we say
∃
!
x
Example
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This note was uploaded on 12/24/2010 for the course CS CS 173 taught by Professor Fleck during the Spring '10 term at University of Illinois, Urbana Champaign.
 Spring '10
 fleck

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