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Xypxy answerfalse 2 xypxy answertrue 3 xy pxy

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Unformatted text preview: is
a
thingamabob
 


“Nothing
is
a
snurd.”
 




Solution:
¬∃x S(x) What is this equivalent to? 




Solution:


∀x ¬ S(x) 
 Transla*on
(cont)
   U
=
{fleegles,
snurds,
thingamabobs}
 F(x):
x
is
a
fleegle
 S(x):
x
is
a
snurd
 T(x):
x
is
a
thingamabob
 

“All
fleegles
are
snurds.”
 


Solution:
∀x (F(x)→ S(x)) Transla*on
(cont)
   U
=
{fleegles,
snurds,
thingamabobs}
 F(x):
x
is
a
fleegle
 S(x):
x
is
a
snurd
 T(x):
x
is
a
thingamabob
 

“Some
fleegles
are
thingamabobs.”
 


Solution:
∃x (F(x) ∧ T(x)) Transla*on
(cont)
   U
=
{fleegles,
snurds,
thingamabobs}
 F(x):
x
is
a
fleegle
 S(x):
x
is
a
snurd
 T(x):
x
is
a
thingamabob
 


“No
snurd
is
a
thingamabob.”
 




Solution:
¬∃x (S(x) ∧ T(x)) What is this equivalent to? 




Solution:
∀x (¬S(x) ∨ ¬T(x))
 Transla*on
(cont)
   U
=
{fleegles,
snurds,
thingamabobs}
 F(x):
x
is
a
fleegle
 S(x):
x
is
a
snurd
 T(x):
x
is
a
thingamabob
 

“If
any
fleegle
is
a
snurd
then
it
is
also
a
thingamabob.”
 




Solution:
∀x ((F(x) ∧ S(x))→ T(x)) System
Specifica*on
Example
   Predicate
logic
is
used
for
specifying
properties
that
systems
must
 satisfy.
   For
example,
translate
into
predicate
logic:
   “Every
mail
message
larger
than
one
megabyte
will
be
 compressed.”
   “If
a
user
is
active,
at
least
one
network
link
will
be
available.”
   Decide
on
predicates
and
domains
(left
implicit
here)
for
the
 variables:
   Let
L(m,
y)
be
“Mail
message
m
is
larger
than
...
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This document was uploaded on 03/06/2014 for the course MATH 320 at CSU Northridge.

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