Practice Direct Proof in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A direct proof starts from assumptions and logically derives the conclusion step by step.
Start from what you know (the hypotheses) and chain logical steps forward until you reach what you want to prove — no detours, no tricks, just forward reasoning.
Example 1
easyProve directly: the sum of an even integer and an odd integer is odd.
Example 2
mediumProve directly: for all real x, (x-1)(x+1) = x^2 - 1.
Example 3
easyProve directly: if x > y > 0, then x^2 > y^2.
Example 4
mediumProve directly: for all integers n, n^2 + n is even.