Contradiction Method Quizzes, Questions & Answers

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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 what you want to prove, follow the...

Questions: 20 | Attempts: 17 | Last updated: May 21, 2026

Sample Question 1
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

Sample Question 2
To prove 'If ab is even, then at least one of a or b is even' by contradiction, what should be assumed?

Ab is even and both a and b are odd

Ab is even and both a and b are even

Ab is odd and both a and b are odd

Ab is odd and both a and b are even

Sample Question 3
In the classical proof that √2 is irrational, where does the contradiction arise?

A/b is not in lowest terms

√2 is actually an integer

A and b are not integers

√2 is not a real number

Recent Contradiction Method Quizzes

Existence, Non-Existence, and Parity via Contradiction

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

Sample Question
What is the key characteristic of a proof by contradiction?

It relies on deriving a contradiction.

It uses direct reasoning.

It avoids assumptions.

It only works for false statements.

Classic Number-Theoretic Proofs by Contradiction

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

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.

Core Ideas of Proof by Contradiction

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

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