Practice Proofs in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

A mathematical proof is a rigorous logical argument that demonstrates the truth of a statement beyond doubt, proceeding from accepted axioms and previously proven results through valid inference rules.

It is not guessing the answer; it is proving why the answer must be true.

Example 1

easy
Prove directly: The sum of two even integers is even.

Example 2

medium
Prove directly: For any integer n, if n is odd then n^2 is odd.

Example 3

medium
Prove: The product of two odd integers is odd.

Example 4

medium
Prove directly: if n is even, then n+1 is odd.