Command Words

Prove

Demonstrate that a statement is always true, using general (often algebraic) reasoning, not specific numbers.

Definition

A "prove" question requires a watertight argument that holds for every case, not just one example. Substituting numbers is not a proof — it is an example. Use letters (n for any integer, 2n for any even number, 2n+1 for any odd) and reason symbolically.

Example

Prove that the sum of two consecutive integers is odd. Let the integers be n and n+1. Their sum is 2n+1, which is odd by definition. QED.

Common confusion

"Show that" usually involves substituting specific numbers. "Prove" needs a general argument.

Used in these topics

Algebraic proof →

Related terms

Show that

You must demonstrate the result starting from given values — the answer is provided, your job is the working.

Hence

Use the previous part of the question to answer this part. You must connect to what you have already found.

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