# Quantifiers and Quantified Statements MCQs with Answers

Quantifiers and Quantified Statements 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 Quantifiers and Quantified Statements MCQs for Preparation.

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## Quantifiers and Quantified Statements Online MCQs with Answers

The symbol ∀ is used to represent which quantifier in logic?
a) Existential quantifier
b) Universal quantifier
c) Conditional quantifier
d) Negation quantifier

b) Universal quantifier

The statement “For every natural number n, n^2 ≥ 0” can be symbolically represented as:
a) ∃n (n^2 ≥ 0)
b) ∃n (n^2 < 0)
c) ∀n (n^2 ≥ 0)
d) ∀n (n^2 < 0)

c) ∀n (n^2 ≥ 0)

a) Existential quantifier
b) Universal quantifier
c) Conditional quantifier
d) Negation quantifier

a) Existential quantifier

The statement “There exists a real number x such that x^2 = 4” can be symbolically represented as:
a) ∃x (x^2 = 4)
b) ∃x (x^2 ≠ 4)
c) ∀x (x^2 = 4)
d) ∀x (x^2 ≠ 4)

a) ∃x (x^2 = 4)

The negation of the statement “For every natural number n, n^2 ≥ 0” is:
a) ∃n (n^2 < 0)
b) ∃n (n^2 ≥ 0)
c) ∀n (n^2 < 0)
d) ∀n (n^2 ≥ 0)

a) ∃n (n^2 < 0)

The negation of the statement “There exists a real number x such that x^2 = 4” is:
a) ∃x (x^2 ≠ 4)
b) ∃x (x^2 = 4)
c) ∀x (x^2 ≠ 4)
d) ∀x (x^2 = 4)

a) ∃x (x^2 ≠ 4)

The quantified statement “∀x ∈ R, x^2 ≥ 0” is:
a) True
b) False
c) Neither true nor false
d) Cannot be determined

a) True

The quantified statement “∃x ∈ Z, x^2 = 4” is:
a) True
b) False
c) Neither true nor false
d) Cannot be determined

a) True

The quantified statement “∀x ∈ N, x^2 < x” is:
a) True
b) False
c) Neither true nor false
d) Cannot be determined

b) False

The quantified statement “∃x ∈ Q, x^2 = 3” is:
a) True
b) False
c) Neither true nor false
d) Cannot be determined

b) False

The quantified statement “∀x ∈ R, ∃y ∈ R, x + y = 0” is:
a) True
b) False
c) Neither true nor false
d) Cannot be determined

a) True

The quantified statement “∃x ∈ Z, ∀y ∈ Z, x + y = 0” is:
a) True
b) False
c) Neither true nor false
d) Cannot be determined

a) True

The quantified statement “∀x ∈ N, ∃y ∈ N, x + y = 10” is:
a) True
b) False
c) Neither true nor false
d) Cannot be determined

a) True

The quantified statement “∃x ∈ Q, ∀y ∈ Q, x + y = 0” is:
a) True
b) False
c) Neither true nor false
d) Cannot be determined

b) False

The quantified statement “∀x ∈ R, ∃y ∈ R, x^2 = y” is:
a) True
b) False
c) Neither true nor false
d) Cannot be determined

a) True

The quantified statement “∃x ∈ Z, ∀y ∈ Z, x^2 = y” is:
a) True
b) False
c) Neither true nor false
d) Cannot be determined

b) False

The quantified statement “∀x ∈ N, ∃y ∈ N, x^2 = y” is:
a) True
b) False
c) Neither true nor false
d) Cannot be determined

b) False

The quantified statement “∃x ∈ Q, ∀y ∈ Q, x^2 = y” is:
a) True
b) False
c) Neither true nor false
d) Cannot be determined

b) False

The quantified statement “∀x ∈ Z, ∃y ∈ Z, x + y = 10” is:
a) True
b) False
c) Neither true nor false
d) Cannot be determined

a) True

The quantified statement “∃x ∈ N, ∀y ∈ N, x + y = 10” is:
a) True
b) False
c) Neither true nor false
d) Cannot be determined

b) False

The quantified statement “∀x ∈ R, ∃y ∈ R, y^2 = x” is:
a) True
b) False
c) Neither true nor false
d) Cannot be determined

a) True

The quantified statement “∃x ∈ Z, ∀y ∈ Z, y^2 = x” is:
a) True
b) False
c) Neither true nor false
d) Cannot be determined

b) False

The quantified statement “∀x ∈ N, ∃y ∈ N, y^2 = x” is:
a) True
b) False
c) Neither true nor false
d) Cannot be determined

b) False

The quantified statement “∃x ∈ Q, ∀y ∈ Q, y^2 = x” is:
a) True
b) False
c) Neither true nor false
d) Cannot be determined

b) False

The quantified statement “∀x ∈ Z, ∃y ∈ Z, y > x” is:
a) True
b) False
c) Neither true nor false
d) Cannot be determined

a) True

The quantified statement “∃x ∈ R, ∀y ∈ R, y > x” is:
a) True
b) False
c) Neither true nor false
d) Cannot be determined

b) False

The quantified statement “∀x ∈ N, ∃y ∈ N, y > x” is:
a) True
b) False
c) Neither true nor false
d) Cannot be determined

a) True

The quantified statement “∃x ∈ Q, ∀y ∈ Q, y > x” is:
a) True
b) False
c) Neither true nor false
d) Cannot be determined

b) False

The quantified statement “∀x ∈ Z, ∃y ∈ Z, x > y” is:
a) True
b) False
c) Neither true nor false
d) Cannot be determined

b) False

The quantified statement “∃x ∈ R, ∀y ∈ R, x > y” is:
a) True
b) False
c) Neither true nor false
d) Cannot be determined

a) True

The quantified statement “∀x ∈ N, ∃y ∈ N, x > y” is:
a) True
b) False
c) Neither true nor false
d) Cannot be determined

b) False

The quantified statement “∃x ∈ Q, ∀y ∈ Q, x > y” is:
a) True
b) False
c) Neither true nor false
d) Cannot be determined