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most important part c) Determining whether a quantified logical statement is true and translating into English, part...

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Advance Math

most important part c)

Determining whether a quantified logical statement is true andtranslating into English, part 2.

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In the following question, the domain of discourse is a set ofmale patients in a clinical study. Define the followingpredicates:

  • P(x): x was given the placebo
  • D(x): x was given the medication
  • A(x): x had fainting spells
  • M(x): x had migraines

Suppose that there are five patients who participated in thestudy. The table below shows the names of the patients and thetruth value for each patient and each predicate:

NameP(x)D(x)A(x)M(x)
FrodoTFFT
GandalfFTFF
GimliFTTF
AragornTFTT
BilboTTFF

For each of the following quantified statements, indicatewhether the statement is a proposition. If the statement is aproposition, give its truth value and translate the expression intoEnglish.

(c) ?x M(x) ? D(x)

(f) ?x ((M(x) ? A(x)) ? ¬D(x))

(g) ?x (D(x) ? ¬A(x) ? ¬M(x))

(h) ?x (D(x) ? (A(x) ? M(x)))

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