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Contrapositive Proof Quizzes, Questions & Answers

Top Trending Contrapositive Proof Quizzes

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, carefully negating phrases like “both are...

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

Sample Question 1
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

Sample Question 2
Proof: "Assume n is even. Then n = 2k, so n² = 4k² = 2(2k²) is even." This proves:

If n is even, then n² is even

If n² is odd, then n is odd

Both A and B

If n² is even, then n is even

Sample Question 3
To prove "If x is irrational, then √x is irrational" by contrapositive, start with:

Assume x is irrational

Assume √x is rational

Assume x is rational

Assume √x is irrational

Recent 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. You’ll explore how reversing and...

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 with Quantifiers, Sets, and Limits

Ready to level up your contrapositive skills in more abstract math? In this quiz, you’ll apply contraposition to statements about sets, intersections, divisibility, factorial inequalities, limits, and...

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

Sample Question
Give the contrapositive of "If x ∈ A ∩ B, then x ∈ 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 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,” inequalities involving squares, and...

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