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Question

Translate the following statement into a logical expression.

•P(x) : x was given the placebo

•D(x) : x was given the medication

•M(x) : x had migraines

 

(b)  Every patient who took the placebo had migraines.  (Hint:  you will need to apply the conditional identity, p→q ≡ ¬p∨q.)

Answer 1

P→M⇒¬P∨M

¬P≡D, so P→M⇒¬P∨M⇒D∨M

(To put this back into words: a patient involved in a clinical trial receives either the medication or a placebo. There are no patients who take neither or both. If the patient receives the placebo, that patient develops migraines. If the patient receives medication, then it cannot be determined whether that patient develops migraines. The results of the clinical test will include all those on medication who developed migraines and all those who received placebos.)