MODULE
ONE
PROBLEM
SET
1
Directions:
Type
your
solutions
into
this
document
and
be
sure
to
show
all
steps
for
arriving
at
your
solution.
Just
giving
a
final
number
may
not
receive
full
credit.
P
ROBLEM
1
In
the
following
question,
the
domain
of
discourse
is
a
set
of
male
patients
in
a
clinical
study.
Define
the
following
predicates:
•
P (x x) : was given the placebo
•
D(x)
:
x
was
given
the
medication
•
M
( )x
:
x
had
migraines
Translate
each
of
the
following
statements
into
a
logical
expression.
Then
negate
the
expression
by
adding
a
negation
operation
to
the
beginning
of
the
expression.
Apply
De
Morgan’s
law
until
each
negation
operation
applies
directly
to
a
predicate
and
then
translate
the
logical
expression
back
into
English.
Sample
question:
Some
patient
was
given
the
placebo
and
the
medication.
•
∃
x
(P
(x)
∧
D(x))
•
Negation:
¬∃
x
(P
( )x
∧
D(x))
•
Applying
De
Morgan’s
law:
A
x
(
¬
P
( )x
∨
¬
