Existential Statements Quizzes, Questions & Answers

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Test Your Knowledge About Existence Theorems

Existence theorems regroup any mathematical or scientific statement beginning with "there exists...", or "for all x,y there exists...", etc. In other words, it is a theorem with a prenex normal form involving...

Questions: 10 | Attempts: 139 | Last updated: Mar 19, 2025

Sample Question 1
What is constructive mathematics?

It is the continuity of a function such as a sin x proven as a constructive bound on the modulus of continuity

It is the stagnation of a function such as a sin x proven as a constructive bound on the modulus of continuity

It is the improvement of a function such as a sin x proven as a constructive bound on the modulus of continuity

It is the continuity of a function such as a tan x proven as a constructive bound on the modulus of continuity

Sample Question 2
What is the axiom of infinity?

It's a very complicated rule.

It's the principle behind plus and minus infinity.

It is 1 of the axioms of Zermelo-Fraenkel set theory.

It is 1 of the axioms of the Newton set theory.

Sample Question 3
What is an existential quantification?

It's a type of function, which is interpreted as "there exists"; "there is at least one", etc.

It's what led to the discovery of the number "0"

It's what helps us give value to numbers.

It's a type of quantifier, a logical constant which is interpreted as "there exists"; "there is at least one", etc.

Recent Existential Statements Quizzes

Existential Statements Quiz: Examine Existence Claims in Logic

Existence claims can open the door to some surprisingly deep ideas, and this existential statements quiz helps you get comfortable working with them. You’ll look at statements that claim something exists, even if...

Questions: 20 | Attempts: 10 | Last updated: Dec 17, 2025

Sample Question
∃x(P(x) ∧ Q(x)) implies (∃x P(x)) ∧ (∃x Q(x)).

True

False

Advanced Existential Reasoning and Quantifier Interactions Quiz

In this quiz, you’ll dive deeper into what it really means to say “there exists” in different domains. You’ll test statements like “There exists a largest integer,” see why some quantifier...

Questions: 15 | Attempts: 11 | Last updated: Jan 28, 2026

Sample Question
∃ x (P(x) ∧ Q(x)) implies (∃ x P(x)) ∧ (∃ x Q(x)).

True

False

Translation, Negation, and Witness Identification Quiz

Think you can keep track of “there exists” when it’s combined with other quantifiers and connectives? This quiz pushes your understanding further by asking you to reason about statements like ∃x P(x) ∨...

Questions: 15 | Attempts: 10 | Last updated: Jan 28, 2026

Sample Question
Which natural language phrase indicates an existential statement?

For all

Some

None

Always

Foundations of Existential Quantifiers Quiz

Ready to get comfortable with the “there exists” symbol in logic? In this quiz, you’ll work with the existential quantifier (∃), learn exactly when a statement like ∃x P(x) is true, and translate...

Questions: 15 | Attempts: 11 | Last updated: Jan 28, 2026

Sample Question
Which symbol represents "there exists"?

∀

∃

→

¬

Existence Theorem Assessment Test

Existence theorems are mathematical theorems with a statement that begins with 'there exist(s)..'. It is a theorem with a prenex normal form involving the existential quantifier. Take this test to find...

Questions: 10 | Attempts: 153 | Last updated: Mar 20, 2025

Sample Question
Find the differential dy of the given function. y= 3x 2 - 4

40x dx

12x dx

6x dx

36x dx