Discrete Mathematics. Determine whether a quantified logical statement is true.

Question

Discrete Mathematics. Determine whether a quantified logical statement is true.

(a)

x (M(x) D(x))

(b)

x M(x) x D(x)

(c)

x M(x) D(x)

(d)

x (A(x) M(x))

(e)

x (M(x) A(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)))

EXERCISE 1.7.6: Determining whether a quantified logical statement is true In the following question, the domain of discourse 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 P(x)D(x) A() MO) Frodo TF F T Gandalf F T F F GimliF T T F Aragorn T F T T BilboT 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.

Explanation / Answer

a)False (No same patient has M(x) and D(x) true)
b) True (M(x) holds for some x and D(x) hods for some x)
c) True
d) False (For all the patients, A(x) and M(x) is not true)
e)False (Not for all the patients, A(x) and M(x) are same)
f) True (Whenever M(x) and A(x) holds then we have not D(x).true for Patient Aragorn
g) True (Patient Gandalf)
h) False (Gandalf violates)

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