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 the study. The table below shows the names of the patients and the truth value for each patient and each predicate
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Exercise 1.7.8: Determining whether a quantified logical statement is true and translating into English, part 2.
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In the following question, the domain is a set of male patients in a clinical study. Define the following predicates:
- 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 the study. The table below shows the names of the patients and the truth 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, indicate whether the statement is a proposition. If the statement is a proposition, give its truth value and translate the expression into English.
(g)
∃x (D(x) ∧ ¬A(x) ∧ ¬M(x))
(h)
∀x (D(x) → (A(x) ∨ M(x)))
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