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).

Name: (a) Every patient was given the medication or the placcbo or both.(b)
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Description: (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 toapply the conditional identity, p → q =pV q.)(c) There is a patient who had migraines and was given the pl

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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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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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.

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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