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:
| Name | P(x) | D(x) | A(x) | M(x) |
|---|
| Frodo | T | F | F | T |
| Gandalf | F | T | F | F |
| Gimli | F | T | T | F |
| Aragorn | T | F | T | T |
| Bilbo | T | T | F | F |
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)))
