Proof Techniques Quizzes, Questions & Answers

Direct Proof Quizzes

Direct Proof in Algebra, Functions, and Sets

Think you can turn everyday math facts into solid proofs? This quiz lets you put that to the test using direct proofs in number theory, algebra, and functions. You’ll write i...

Questions: 15 | Attempts: 13 | Last updated: Dec 12, 2025

Sample Question
In a direct proof that "If a|b and b|c, then a|c" (where | means divides), which is the first appropriate statement?

Assume a|c

Assume a|b and b|c

Let b = ak and c = bm for integers k,m

Let c = an for some integer n

Direct Proof Quiz: Strengthen Step-by-Step Logical Arguments

Direct reasoning is the foundation of most mathematical arguments, and this direct proof quiz helps you practice it in a clear, approachable way. You’ll work through statemen...

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

Sample Question
In proving "If a relation R is symmetric and transitive, and every element is related to at least one element, then R is reflexive" directly, we need to:

Assume aRa is false for some a

Prove the contrapositive statement

Use induction on the number of elements

For each a, find b such that aRb, then use symmetry and transitivity to show aRa

Direct Proof Basics: From Hypothesis to Conclusion

Are you ready to see how formal proofs actually work step by step? In this quiz, you’ll practice the core idea of a direct proof: start by assuming the hypothesis is true and...

Questions: 15 | Attempts: 10 | Last updated: Dec 12, 2025

Sample Question
What is the first step in a direct proof of "If P, then Q"?

Assume Q is true

Assume P is true

Assume P is false

Assume Q is false

All Direct Proof Quizzes

Contrapositive Proof Quizzes

Contrapositive Proof Quiz: Rewrite and Prove Logical Implications

Contrapositive reasoning transforms a statement into a form that’s often much easier to prove, and this contrapositive proof quiz shows you why that approach is so effective....

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

Sample Question
What is the contrapositive of: 'If x belongs to A ∩ B, then x belongs to A'?

If x ∉ A, then x ∉ (A ∩ B)

If x ∈ A, then x ∈ (A ∩ B)

If x ∉ (A ∩ B), then x ∉ A

If x ∈ (A ∩ B), then x ∉ A

Contrapositive Fundamentals: Logic, Parity, and Common Pitfalls

Are you ready to see how “flipping” a statement can actually make it easier to prove? In this quiz, you’ll practice turning an implication into its contrapositive...

Questions: 15 | Attempts: 10 | Last updated: Dec 12, 2025

Sample Question
To prove "If ab is odd, then a and b are odd" by contrapositive, show:

If a or b is even, then ab is even

If ab is even, then a or b is even

If a and b are even, then ab is even

If a is odd, then ab is odd

Contrapositive in Calculus and Number Theory

Think you can handle proofs that mix logic with calculus and algebra? This quiz lets you test that by working with classic results like “differentiable implies continuous,&rd...

Questions: 15 | Attempts: 10 | Last updated: Dec 12, 2025

Sample Question
Which statement is the contrapositive of "If a function f is differentiable at x = c, then f is continuous at x = c"?

If a function f is continuous at x = c, then f is differentiable at x = c

If a function f is not continuous at x = c, then f is not differentiable at x = c

If a function f is not differentiable at x = c, then f is not continuous at x = c

If a function f is discontinuous at x = c, then f is differentiable at x = c

All Contrapositive Proof Quizzes

Contradiction Method Quizzes

Proof by Contradiction Quiz: Expose Logical Inconsistencies

Proof by contradiction can feel like a clever puzzle, and this contradictions proof quiz lets you practice the method in a clear, intuitive way. You’ll assume the opposite of...

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

Sample Question
What is the defining feature of a proof by contradiction?

You assume the negation and derive an impossibility

You avoid assumptions entirely

You prove the statement directly

You rely only on examples

Core Ideas of Proof by Contradiction

Are you ready to flip your thinking and start a proof from the “wrong” side on purpose? In this quiz, you’ll learn how proof by contradiction works by assuming th...

Questions: 15 | Attempts: 10 | Last updated: Dec 12, 2025

Sample Question
What is the primary goal of assuming the negation in a proof by contradiction?

To prove the negation true

To derive a contradiction

To avoid direct proof

To simplify the problem

Classic Number-Theoretic Proofs by Contradiction

Think you can handle some of the most famous “impossible” proofs in math? This quiz lets you practice proof by contradiction on classic results from number theory and a...

Questions: 15 | Attempts: 10 | Last updated: Dec 12, 2025

Sample Question
What is the first step in a proof by contradiction?

Assume the negation of the statement is true.

Assume the statement is true.

Prove the statement directly.

Find a counterexample.

All Contradiction Method Quizzes

Inductive Proof Quizzes

Inductive Proof Quiz: Practice Mathematical Induction Basics

Induction turns patterns into solid arguments, and this inductive proof quiz helps you build that skill step by step. You’ll start with base cases, move through inductive ass...

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

Sample Question
Mathematical induction is primarily designed to prove statements about which set of numbers?

All real numbers

The natural numbers (1,2,3,...)

All complex numbers

All rational numbers

Foundations of Mathematical Induction Quiz

Curious how one simple idea can prove infinitely many cases at once? In this quiz, you’ll explore the core structure of mathematical induction: checking a base case, assuming...

Questions: 15 | Attempts: 10 | Last updated: Dec 16, 2025

Sample Question
Mathematical induction is primarily used to prove statements about which set of numbers?

The natural numbers

All real numbers

All integers

All rational numbers

Summations, Inequalities, and Exponential Induction Quiz

Think you can turn patterns into rock-solid proofs? This quiz gives you plenty of chances to do that using induction on classic algebra and number theory statements. You’ll w...

Questions: 15 | Attempts: 10 | Last updated: Dec 12, 2025

Sample Question
To prove 1+2+…+n = n(n+1)/2, what is the statement P(k)?

1+2+…+k = k(k+1)/2

1+2+…+n = n(n+1)/2

1+2+…+(k+1) = (k+1)(k+2)/2

1 = 1(2)/2

All Inductive Proof Quizzes

Case Analysis Quizzes

Fundamentals of Proof by Cases

Want to get comfortable breaking proofs into clear, logical pieces? In this quiz, you’ll practice using exhaustive, mutually exclusive cases to show a conclusion must hold in...

Questions: 15 | Attempts: 12 | Last updated: Dec 12, 2025

Sample Question
Proof by case analysis requires cases to be what?

Exhaustive and mutually exclusive

Exhaustive only

Mutually exclusive only

Optional

Exhaustive and Mutually Exclusive Case Splits

Ready to see how case analysis really shines in number theory problems? In this quiz, You’ll work with splits like “n is even or odd” and “n mod k = 0, 1, &...

Questions: 15 | Attempts: 12 | Last updated: Dec 12, 2025

Sample Question
To prove “If n is integer, then n(n+1) is even,” you should split on:

N is even or odd

N is prime

N is positive

No split needed

Case Analysis on Integers and Real Numbers

Are you ready to apply case analysis numbers reasoning? In this quiz, you’ll focus on case splits over the real numbers and on recognizing good vs. bad case structures. You&r...

Questions: 15 | Attempts: 12 | Last updated: Dec 12, 2025

Sample Question
A case analysis that splits on “n is divisible by 3” and “n is not divisible by 3” is:

Exhaustive

Not exhaustive

Overlapping

Invalid

All Case Analysis Quizzes

Counterexamples Quizzes

Basics of Counterexamples and Disproving Universal Statements

Ready to see how one clever example can break a big “for all” claim? In this quiz, you’ll practice using counterexamples to take down universal statements about n...

Questions: 15 | Attempts: 11 | Last updated: Dec 12, 2025

Sample Question
What is the purpose of a counterexample?

To disprove a universal statement

To simplify a proof

To prove an existential statement

To prove a statement is true

Counterexamples in Number Theory, Geometry, and Functions

Think you can outsmart overconfident math statements? In this quiz, you’ll use counterexamples to challenge claims from algebra, geometry, and calculus-style topics. You&rsqu...

Questions: 15 | Attempts: 11 | Last updated: Dec 12, 2025

Sample Question
Counterexample to "All triangles have equal sides":

Square

Circle

Scalene

Equilateral

Counterexamples in Sets, Conditionals, and Everyday Statements

Ready for counterexamples at a more abstract level? This quiz takes you into sets, limits, sequences, and logical statements. You’ll challenge claims like “all subsets ...

Questions: 15 | Attempts: 11 | Last updated: Dec 16, 2025

Sample Question
Counterexample to "All subsets are proper":

Empty subset

Singleton

Power set

The set itself

All Counterexamples Quizzes

Top Trending Proof Techniques Quizzes

Proof Techniques Math Quiz

Questions: 8 | Attempts: 12 | Last updated: Nov 17, 2025

Sample Question 1
What is the purpose of a proof in mathematics?

To provide a visual representation

To establish the truth of a statement

To confuse the reader

To summarize a topic

Sample Question 2
Which of the following is a common proof technique?

Induction

Extrapolation

Estimation

Observation

Sample Question 3
What does proof by contradiction involve?

Assuming the statement is true

Assuming the statement is false

Using examples

Drawing diagrams

Proof Techniques Quizzes, Questions & Answers

Popular Proof Techniques Topics

Direct Proof Quizzes

Contrapositive Proof Quizzes

Contradiction Method Quizzes

Inductive Proof Quizzes

Case Analysis Quizzes

Counterexamples Quizzes

Top Trending Proof Techniques Quizzes

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