Practice Proof (Intuition) in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The informal, intuitive sense of why a mathematical statement must be true — the "aha" that precedes and motivates a formal proof.
A chain of reasoning that convinces you something MUST be true.
Example 1
easyBefore writing a formal proof that 'the sum of two even integers is even,' build the intuition. Explain why it must be true, then formalise.
Example 2
mediumBuild intuition for why \sqrt{2} is irrational before writing the formal proof. What is the core contradiction?
Example 3
easyBuild intuition for the statement: 'For any integer n, n(n+1) is even.' Explain informally why this must be true.
Example 4
mediumBuild intuition for induction: why does proving 'P(k) \Rightarrow P(k+1)' together with P(1) establish P(n) for all n?