snhu
MODULE ONE PROBLEM SET
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Jeffrey Scroggins
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
(b) Vx(P(r))V D(X)
(c) negation: -Vx (Px) V D(x)
(d) de Morgan law 3x (p(x)) V D(x)
(e) English: most patient has taken medication while some took placebo
(f) Every patient who took the placebo had migraines. (Hint: you will need to apply the conditional identity, p q = -p V q.)
(g) Vx P(x)M(x)
(h)-Vx-P(x)M(x)
(i) 3x P(x)V-M(x)
(j) There is a patient who had migraines and was given the placebo.
(k) 3M(x)AP(x)
(l) -3M(x)AP(x)
(m) Vx(-M(x)/vee-P(x))
(n) english: most patients didnt have a migraine and were not given placebo fo