In: Advanced Math
most important part c)
Determining whether a quantified logical statement is true and translating into English, part 2.
infoAbout
In the following question, the domain of discourse is a set of male patients in a clinical study. Define the following predicates:
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.
(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)))