# Predicate Logic MCQs with Answers

Predicate Logic MCQs are very important test and often asked by various testing services and competitive exams around the world. Here you will find all the Important Predicate Logic MCQs for Preparation.

The student can clear their concepts for Predicate Logic online quiz by attempting it. Doing MCQs based Predicate Logic will help you to check your understanding and identify areas of improvement.

## Predicate Logic Online MCQs with Answers

Predicate logic extends propositional logic by introducing:
a) Variables
b) Connectives
c) Truth tables
d) Quantifiers

a) Variables

In predicate logic, a predicate is:
a) A statement that is always true.
b) A statement that is always false.
c) A function that maps variables to values.
d) A statement that depends on one or more variables.

d) A statement that depends on one or more variables.

The quantifiers used in predicate logic are:
a) ∃ (exists) and ∀ (for all)
b) ∨ (or) and ∧ (and)
c) ⊃ (implies) and ¬ (not)
d) ⊕ (exclusive or) and ↔ (if and only if)

a) ∃ (exists) and ∀ (for all)

The symbol ∃ is read as:
a) And
b) Not
c) There exists
d) For all

c) There exists

The symbol ∀ is read as:
a) And
b) Not
c) There exists
d) For all

d) For all

The statement “There exists an x such that P(x)” can be symbolically represented as:
a) ∃x P(x)
b) ∃x ¬P(x)
c) ∀x P(x)
d) ∀x ¬P(x)

a) ∃x P(x)

The statement “For all x, P(x)” can be symbolically represented as:
a) ∃x P(x)
b) ∃x ¬P(x)
c) ∀x P(x)
d) ∀x ¬P(x)

c) ∀x P(x)

The statement “There exists an x such that ¬P(x)” can be symbolically represented as:
a) ∃x P(x)
b) ∃x ¬P(x)
c) ∀x P(x)
d) ∀x ¬P(x)

b) ∃x ¬P(x)

The statement “For all x, ¬P(x)” can be symbolically represented as:
a) ∃x P(x)
b) ∃x ¬P(x)
c) ∀x P(x)
d) ∀x ¬P(x)

d) ∀x ¬P(x)

The negation of the statement “∃x P(x)” is:
a) ∃x P(x)
b) ∃x ¬P(x)
c) ∀x P(x)
d) ∀x ¬P(x)

d) ∀x ¬P(x)

The negation of the statement “∀x P(x)” is:
a) ∃x P(x)
b) ∃x ¬P(x)
c) ∀x P(x)
d) ∀x ¬P(x)

b) ∃x ¬P(x)

The quantified statement “∀x (P(x) → Q(x))” can be read as:
a) For every x, P(x) or Q(x).
b) There exists an x such that P(x) implies Q(x).
c) For all x, if P(x) then Q(x).
d) There exists an x such that P(x) and Q(x).

c) For all x, if P(x) then Q(x).

The quantified statement “∃x (P(x) ∧ Q(x))” can be read as:
a) For every x, P(x) or Q(x).
b) There exists an x such that P(x) implies Q(x).
c) For all x, if P(x) then Q(x).
d) There exists an x such that P(x) and Q(x).

d) There exists an x such that P(x) and Q(x).

The quantified statement “∀x (P(x) ∨ Q(x))” can be read as:
a) For every x, P(x) or Q(x).
b) There exists an x such that P(x) implies Q(x).
c) For all x, if P(x) then Q(x).
d) There exists an x such that P(x) and Q(x).

a) For every x, P(x) or Q(x).

The quantified statement “∃x (P(x) → Q(x))” can be rewritten as:
a) ∀x (P(x) ∨ Q(x))
b) ¬∀x (P(x) ∨ Q(x))
c) ∀x (P(x) → Q(x))
d) ¬∃x (P(x) ∨ Q(x))

d) ¬∃x (P(x) ∨ Q(x))

The quantified statement “∀x (P(x) ∧ Q(x))” can be rewritten as:
a) ∃x (P(x) ∨ Q(x))
b) ¬∃x (P(x) ∨ Q(x))
c) ∃x (P(x) ∧ Q(x))
d) ¬∀x (P(x) ∨ Q(x))

c) ∃x (P(x) ∧ Q(x))

The quantified statement “∀x (P(x) ∨ Q(x))” can be rewritten as:
a) ∃x (P(x) ∨ Q(x))
b) ¬∃x (P(x) ∨ Q(x))
c) ∃x (P(x) ∧ Q(x))
d) ¬∀x (P(x) ∨ Q(x))

a) ∃x (P(x) ∨ Q(x))

The quantified statement “∃x (P(x) → Q(x))” can be rewritten as:
a) ∀x (P(x) ∨ Q(x))
b) ¬∀x (P(x) ∨ Q(x))
c) ∀x (P(x) → Q(x))
d) ¬∃x (P(x) ∨ Q(x))

c) ∀x (P(x) → Q(x))

The quantified statement “∃x (P(x) ∧ Q(x))” can be rewritten as:
a) ∀x (P(x) ∨ Q(x))
b) ¬∀x (P(x) ∨ Q(x))
c) ∀x (P(x) → Q(x))
d) ¬∃x (P(x) ∨ Q(x))

c) ∀x (P(x) → Q(x))

The quantified statement “∀x (P(x) ∧ Q(x))” can be rewritten as:
a) ∃x (P(x) ∨ Q(x))
b) ¬∃x (P(x) ∨ Q(x))
c) ∃x (P(x) ∧ Q(x))
d) ¬∀x (P(x) ∨ Q(x))

a) ∃x (P(x) ∨ Q(x))

The negation of the statement “∀x (P(x) ∧ Q(x))” is:
a) ∃x (P(x) ∨ Q(x))
b) ¬∃x (P(x) ∨ Q(x))
c) ∀x (P(x) ∨ Q(x))
d) ¬∀x (P(x) ∨ Q(x))