Practice Proof Techniques in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Proof techniques are standard strategies for establishing mathematical claims under different structures.
Choose the argument tool that matches the claim type and assumptions.
Example 1
easyName four proof techniques, give a one-sentence description of each, and identify which is best suited to prove: 'For all n \ge 1, 3 \mid (n^3 - n).'
Example 2
mediumCompare direct proof and proof by contrapositive for: 'If n^2 is even, then n is even.' Which technique is more natural here?
Example 3
easyWhich proof technique is most appropriate for: 'There exists a real number x such that x^2 = 2'? Apply it.
Example 4
mediumProve using mathematical induction: 3^n > 2n+1 for all n \ge 2.