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. Thomas Bagnardi 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).
snhu (a) Every patient was given the medication or the placebo or both. • forallx (D(x) V P(x)) · Negation: - Vx (D(x) V P(x)) · Applying De Morgan's law: 3x (-D(x) A -P(x)) · English: There is a patient who was not given the medication and not given the placebo. (b) Every patient who took the placebo had migraines. (Hint: you will need to apply the conditional identity, p -> q = p V q.) . Vx (P(x) -> M(x)) · Negation: - Vx (P(x) -> M(x)) · Applying Conditional Identity: (P(x) > M(x) = (-P(x) V -M(x) · Applying Double Negation: - P(x) = P(x) . Applying De Morgan's law: 3x (P(x) A -M(x)) · English: Some patient took the placebo and did not have migraines. (c) There is a patient who had migraines and was given the placebo. . Ex (M(x) \ P(x)) . Negation: - 3x (M(x) \ P(x)) . Applying De Morgan's law: Vx (-M(x) V -P(x)) · English: Every patient did not have migraines or did not take the placebo.