MODULE ONE PROBLEM SET
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Jacqueline Amoah
1
Directions: Type your solutions into this document sure show all steps and be to
for arriving your solution. Just giving a final number may not receive full credit.at
P
ROBLEM
1
In the following question, the domain of
discourse
is in a set male patients of a
clinical study. Define the following predicates:
•
P (x) : was given the placebox
•
D(x) : was given the medicationx
•
M (x) : had migrainesx
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
M
o
r
ga
n
’s
law:
∀
x
(
¬
P
(
x
)
∨
¬
D
(
x
))
English: Every patient was either given the placebo given the not or not
medication (or both).
•
∃ ¬ ∧ ¬
