snhu
MODULE ONE PROBLEM SET
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John Smith
snhu
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.
PROBLEM 1
In the following question, the domain of discourse is a set of male patients in a clinical study. Define the following predicates:
P() : was given the placebo
: D(r) : x was given the medication
: M(r) : 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.
:3x(P(x) A D(x))
: Negation: -3x (P(x) A D(x))
: Applying De Morgan's law: Vx (-P(x) V -D(x))
: English: Every patient was either not given the placebo or not given the medication (or both).
snhu
(a) Every patient was given the medication or the placebo or both.
Vx(D(x) V P(x) V(D(r)AP(x))
-Vx(D(x) V P(x) V(D(x)^P(x))
3x(-D(x) A -P(x)A-(D(x)^P(x)))
Some patients were not given the medication and not given the placebo (and not given both).
(b) Every patient who took the placebo had migraines. (Hint: you will need to apply the conditional identity, p q = -p V q
((x)W^(x)d-=(x)W(x)d)xA
-Vx(P(x)M(x)=-P(x)V M(x))
3x(P(x)^-M(x)=P(x)^-M(x))
Some patients took the placebo and did not get a migraine
(c) There is a patient who had migraines and was given the placebo.
3x(M(x)^P(x))
-3x(M(x)AP(x))
Vx(-M(x)V-P(x))
Every patient either did not have migraines or did not take the placebo