COT Final Answers (Questions With Complete Solutions)
∀x∀y∃z (x - y < z) has the same truth value as ___.
p2
¬∀x ∀y ∃z (x + y ≥ z) has the same truth value as ___. Correct
Answers ¬∃x∃y∀z (x - y ≥ z)
p2
¬¬∃x ∃y ∀z (x + y < z)
∀x∃y∃z P(x, y, z) has the same truth value as ___. Correct
Answers ¬∃x∀y∀z ¬P(x, y, z)
¬∀x ∀y ∃z (x + y ≥ z) has the same truth value as ___. Correct
Answers ¬¬∃x ∃y ∀z (x + y < z)
¬∀x∀y A(x, y) has the same truth value as ___.
p2
¬∃x∃y P(x, y) has the same truth value as ___. Correct Answers
∃x¬∀y A(x, y)
p2
∀y ¬∃x P(x, y)
A formula is in conjunctive normal form, or CNF, if and only if
it is a conjunction of disjunctions of literals. Correct Answers
True
Assuming that the domain of discourse is the set of real numbers
select the expression that represents the given mathematical
sentence.
The quotient of two positive numbers is a positive number.
, The product of two negative numbers is a positive number.
Correct Answers ∀x ∀y ((x > 0 ˄ y > 0) → (x/y > 0))
P2: ∀x ∀y ((x < 0 ˄ y < 0) → (xy > 0))
Consider the first-order logic formula
∀x P(a, x) ˅ ∀y P(y, b)
and the interpretation
domain D = {4, 5, 6}, P = {(4, 4), (4, 5), (5, 5), (6, 5), (6, 6)}, a
= 4, b = 5
Select the value of b that makes the formula true. Correct
Answers 5
Consider the FOL formula
∀x (P(x, a) ˄ Q(x, b))
where P, Q are relations and a, b are constants. Which options
represent well-defined interpretations of the formula? Select all
that apply.
∀x (P(x, a) ˄ Q(x, b))?? Correct Answers Domain of discourse
= {Red, Green, Orange, Blue}, a = Red, b = Orange, P =
{(Orange, Red), (Blue, Blue), (Blue, Red)}, Q = {(Red,
Orange), (Green, Orange), (Green, Blue)}
P2
Domain of discourse = {Marion, Robin}, a = Marion, b = Robin,
P = {(Robin, Robin), (Robin, Marion)}, Q ={(Marion, Robin),
(Marion, Marion)}
Domain of discourse = {1, 2, 3}, a = 1, b = 2, P = {(1, 2) (2, 1)},
Q ={(1, 3)}
∀x∀y∃z (x - y < z) has the same truth value as ___.
p2
¬∀x ∀y ∃z (x + y ≥ z) has the same truth value as ___. Correct
Answers ¬∃x∃y∀z (x - y ≥ z)
p2
¬¬∃x ∃y ∀z (x + y < z)
∀x∃y∃z P(x, y, z) has the same truth value as ___. Correct
Answers ¬∃x∀y∀z ¬P(x, y, z)
¬∀x ∀y ∃z (x + y ≥ z) has the same truth value as ___. Correct
Answers ¬¬∃x ∃y ∀z (x + y < z)
¬∀x∀y A(x, y) has the same truth value as ___.
p2
¬∃x∃y P(x, y) has the same truth value as ___. Correct Answers
∃x¬∀y A(x, y)
p2
∀y ¬∃x P(x, y)
A formula is in conjunctive normal form, or CNF, if and only if
it is a conjunction of disjunctions of literals. Correct Answers
True
Assuming that the domain of discourse is the set of real numbers
select the expression that represents the given mathematical
sentence.
The quotient of two positive numbers is a positive number.
, The product of two negative numbers is a positive number.
Correct Answers ∀x ∀y ((x > 0 ˄ y > 0) → (x/y > 0))
P2: ∀x ∀y ((x < 0 ˄ y < 0) → (xy > 0))
Consider the first-order logic formula
∀x P(a, x) ˅ ∀y P(y, b)
and the interpretation
domain D = {4, 5, 6}, P = {(4, 4), (4, 5), (5, 5), (6, 5), (6, 6)}, a
= 4, b = 5
Select the value of b that makes the formula true. Correct
Answers 5
Consider the FOL formula
∀x (P(x, a) ˄ Q(x, b))
where P, Q are relations and a, b are constants. Which options
represent well-defined interpretations of the formula? Select all
that apply.
∀x (P(x, a) ˄ Q(x, b))?? Correct Answers Domain of discourse
= {Red, Green, Orange, Blue}, a = Red, b = Orange, P =
{(Orange, Red), (Blue, Blue), (Blue, Red)}, Q = {(Red,
Orange), (Green, Orange), (Green, Blue)}
P2
Domain of discourse = {Marion, Robin}, a = Marion, b = Robin,
P = {(Robin, Robin), (Robin, Marion)}, Q ={(Marion, Robin),
(Marion, Marion)}
Domain of discourse = {1, 2, 3}, a = 1, b = 2, P = {(1, 2) (2, 1)},
Q ={(1, 3)}
