P2.1 - Proof

Understand and use the structure of mathematical proof, proceeding from given assumptions through a series of logical steps to a conclusion; use methods of proof stated below:.

Use structure of mathematical proof to connect the rule to the data and decision in the question.

This matters because structure of mathematical proof determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply structure of mathematical proof to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Structure of mathematical proof is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Proof by exhaustion Proof by exhaustion.; This involves trying all the options.; Suppose x and y are odd integers less than 7.; Prove that their sum is divisible by 2.

Use proof by exhaustion to connect the rule to the data and decision in the question.

This matters because proof by exhaustion determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply proof by exhaustion to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Proof by exhaustion is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Disproof by counter example.; Disproof by counter example – show that the statement “n2 − n + 1 is a prime number for all values of n” is untrue.

Use disproof by counter example to connect the rule to the data and decision in the question.

This matters because disproof by counter example determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply disproof by counter example to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Disproof by counter example is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.