lecture notes10

Teacheschanx producestheresponse x kevin x kiko no

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Unformatted text preview: 
a
student
in
your
class
who
 has
not
taken
calculus.”
 Symbolically ¬∀x J(x) and ∃x ¬J(x) are equivalent Nega*ng
Quan*fied
Expressions
 (con#nued)
   Now
Consider
∃ x J(x)
 “There
is
a
student
in
this
class
who
has
taken
a
course
in
 Java.” Where
J(x)

is
“x
has
taken
a
course
in
Java.”
   Negating
the
original
statement
gives
“It
is
not
the
 case
that
there
is
a
student
in
this
class
who
has
taken
 Java.”
This
implies
that
“Every
student
in
this
class
has
 not
taken
Java”
 Symbolically ¬∃ x J(x) and ∀ x ¬J(x) are equivalent De
Morgan’s
Laws
for
Quan*fiers
   The
rules
for
negating
quantifiers
are:
   The
reasoning
in
the
table
shows
that:
   These
are
important.
You
will
use
these.

 Transla*on
from
English
to
Logic
 Examples:
 1.  “Some
student
in
this
class
has
visited
Mexico.”
 


Solution:
Let
M(x)
denote
“x
has
visited
Mexico”
and
 S(x)
denote
“x
is
a
student
in
this
class,”

and
U be all people.
 





















∃x (S(x) ∧ M(x))
 2.  “Every
student
in
this
class
has
visited
Canada
or
 Mexico.”
 

Solution:
Add
C(x)
denoting
“x
has
visited
Canada.”
 ∀x (S(x)→ (M(x)∨C(x))) Some
Fun
with
Transla*ng
from
 English
into
Logical
Expressions
   U
=
{fleegles,
snurds,
thingamabobs}
 F(x):
x
is
a
fleegle
 S(x):
x
is
a
snurd
 T(x):
x
is
a
thingamabob
 


Translate
“Everything
is
a
fleegle”
 



Solution:
∀x F(x) Transla*on
(cont)
   U
=
{fleegles,
snurds,
thingamabobs}
 F(x):
x
is
a
fleegle
 S(x):
x
is
a
snurd
 T(x):
x...
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This document was uploaded on 03/06/2014 for the course MATH 320 at CSU Northridge.

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