snhu
MODULE ONE PROBLEM SET
This document is proprietary to Southern New Hampshire University. It and the problems within may not be posted on any non-SNHU website.
ALFREDO ROMERO
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(P(x)V D(x))
: negation: -Vx(P(r)V D(x))
: applying Morgan's law: 3x (- P(x) A - D(x))
: English: Some patient was either not given the placebo and not given medication.
(b) Every patient who took the placebo had migraines. (Hint: you will need to
Vx(P(x) M(x))= Vx(-P(x) V M(x))
negation: -Vx(-P(x)V M(x))
applying Morgan's law: 3x (P(x) A - M(x))
: English: Every patient that took the medication may not have mi graines.
(c) There is a patient who had migraines and was given the placebo.
:3x(M(r)X P(x))
: negation: -x(M(x)^ P(x))
: applying Morgan's law: Vx (- M(r) V - P(r))
: English: every patient either had not migrains or was not given the placebo (or both