Direct Proof Quizzes, Questions & Answers

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Direct Proof in Advanced Structures and Mappings

Direct Proof In Advanced Structures And Mappings

Ready to level up your proof skills in more abstract settings? In this quiz, you’ll use direct proofs to explore sets, relations, sequences, and algebraic structures like rings. You’ll practice showing when one set is...

Questions: 15 | Attempts: 10 | Last updated: Dec 1, 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 in Algebra, Functions, and Sets

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 integers as multiples, express rational numbers as...

Questions: 15 | Attempts: 10 | Last updated: Dec 1, 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 Basics: From Hypothesis to Conclusion

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 then use logic, definitions, and simple algebra...

Questions: 15 | Attempts: 10 | Last updated: Dec 1, 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

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