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Solutionx sx what is this equivalent to solutionx sx

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Unformatted text preview: But if P(x)
is
the
statement
“x
<
2”,
then

both
∃x P(x)


and












 ∀ x P(x) are false. 
 1.  Precedence
of
Quan*fiers
   The
quantifiers
∀
and

∃
have
higher
precedence
than
 all
the
logical
operators.
   For
example,
∀x P(x) ∨ Q(x) means (∀x P(x))∨ Q(x)


   ∀x (P(x) ∨ Q(x)) means something different.   Unfortunately, often people write ∀x P(x) ∨ Q(x) when they mean ∀ x (P(x) ∨ Q(x)). 
 Transla*ng
from
English
to
Logic
 Example
1:

Translate
the
following
sentence
into
predicate
 logic:
“Every
student
in
this
class
has
taken
a
course
in
 Java.”
 Solution:
 

First
decide
on
the
domain
U.

 Solution
1:
If
U
is
all
students
in
this
class,
define
a
 propositional
function
J(x)
denoting
“x
has
taken
a
course
in
 Java”
and
translate
as
∀x J(x). Solution
2: But
if
U
is
all
people,
also
define
a
propositional

 function
S(x)
denoting
“x
is
a
student
in
this
class”
and
 translate
as




∀x (S(x)→ J(x)). ∀x (S(x) ∧ J(x)) is not correct. What does it mean? Transla*ng
from
English
to
Logic
 Example
2:
Translate
the
following
sentence
into
 predicate
logic:
“Some
student
in
this
class
has
taken
 a
course
in
Java.”

 Solution:
 First
decide
on
the
domain
U.

 Solution
1:
If
U
is
all
students
in
this
class,
translate
as

 ∃x J(x) Solution
1:
But
if
U
is
all
people,
then
translate
as
















 ∃x (S(x) ∧ J(x)) ∃x (S(x)→ J(x)) is not correct. What does it mean?
 Returning
to
the
Socrates
Example

   Introduce
the

propositional
functions
Man(x)
 denoting
“x
is
a
man”
and

Mortal(x)
denotin...
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This document was uploaded on 03/06/2014 for the course MATH 320 at CSU Northridge.

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