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In the following question, the domain of discourse is a set of male patients in a clinical study. Define the following predicates: • P(z) : z was given the placebo • D[z) : # was given the medication • M(x): # had migraines Translate cach 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'w law until cach 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. ar (P(x) ^ D(z)) Negation: ¬ar (P(z) ^ D(z)) Applying De Morgan's law: Vz (¬P(x) v ¬D(z)) English: Every patient was either not given the placebo or not given the medication (or both).

In the following question, the domain of discourse is a set of male patients in a clinical study. Define the following predicates: • P(z) : z was given the placebo • D[z) : # was given the medication • M(x): # had migraines Translate cach 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'w law until cach 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. ar (P(x) ^ D(z)) Negation: ¬ar (P(z) ^ D(z)) Applying De Morgan's law: Vz (¬P(x) v ¬D(z)) English: Every patient was either not given the placebo or not given the medication (or both).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(a) Every patient was given the medication or the placcbo or both. (b) Every patient who took the placebo had migraines. (Hint: you will need to apply the conditional identity, p → q =pV q.) (c) There is a patient who had migraines and was given the placebo.
Transcribed Image Text:(a) Every patient was given the medication or the placcbo or both. (b) Every patient who took the placebo had migraines. (Hint: you will need to apply the conditional identity, p → q =pV q.) (c) There is a patient who had migraines and was given the placebo.
In the following question, the domain of discourse is a set of male patients in a clinical study. Define the following predicates: • P(z) : z was given the placebo • D(z) : z was given the medication • M(z): z had migraines Translate cach 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 cach negation operation applices directly to a predicate and then translate the logical expression back into English. Sample question: Some patient was given the placebo and the medication. 3r (P(z) ^ D(z)) • Negation: ¬ar (P(z) ^ D(z)) Applying De Morgan's law: ¥z (¬P(z) V ¬D(z)) English: Every patient was either not given the placebo or not given the medication (or both).
Transcribed Image Text:In the following question, the domain of discourse is a set of male patients in a clinical study. Define the following predicates: • P(z) : z was given the placebo • D(z) : z was given the medication • M(z): z had migraines Translate cach 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 cach negation operation applices directly to a predicate and then translate the logical expression back into English. Sample question: Some patient was given the placebo and the medication. 3r (P(z) ^ D(z)) • Negation: ¬ar (P(z) ^ D(z)) Applying De Morgan's law: ¥z (¬P(z) V ¬D(z)) English: Every patient was either not given the placebo or not given the medication (or both).
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