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. Your Name Here 1
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(x) : x was given the placebo · D(x) : x was given the medication · M(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. . Ex (P(x) A D(x)) . Negation: - 3x (P(x) \ 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).
(a) Every patient was given the snhu medication or the placebo or both. Logical Expression: Vx(D(x) V P(x) V(P(x) AQ(x)) Negation: - Vx(D(x) V P(x)V(P(x) AQ(x)) 3x(-D(x) A-Q(x) A (-D(x) V-Q(x))) De Morgan's Law: 3x(-(D(x) A-P(x)) There is at least one patient who was not give the medication, placebo, or both. (b) Every patient who took the placebo had migraines. (Hint: you will need to apply the conditional identity, p -> q = p V q.) Logical Expression: Vx(P(x) -> M(x)) Negation: - Vx(P(x) -> M(x)) Conditional Identity: - Vx(P(x) VQ(x)) Negation: 3x-(-P(x) V Q(x)) De Morgrgan's Law: 3x(P(x) A-Q(x)) English: At least one patient took the placebo and did not have migraines. (c) There is a patient who had migraines and was given the placebo. Logical Expresvsion: 3x(M(x) \P(x)) Negation: - 3x(M(x) \P(x)) De Morgan's Law: Vx(-M(x) V P(x)) English: Every patient did not take the placebo or did not have migraines.