Year 11 · Specialist Mathematics

The nature of proof

Free examples and worked answers. No account needed.

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Practise the method.

Identify valid arguments and use counterexamples.

Example 1

Illustrative groups of the given unit; compare individual groups with larger bundles.Illustrative positive integer casesm groups, each of size 121212Look for a case that breaks a universal claim.
Compare groups with the larger bundle. Examples do not prove the general statement; one counterexample can disprove it.
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Answer:

Example 2

Two example collections of equal-sized groups.Illustrative positive integer casesm groups of 111111n groups of 11111111Can you regroup without changing group size?
Regroup these positive examples. The question includes all integers: examples do not prove the general statement.
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Answer:

Example 3

Illustrative groups of the given unit; compare individual groups with larger bundles.Illustrative positive integer casesm groups, each of size 666Look for a case that breaks a universal claim.
Compare groups with the larger bundle. Examples do not prove the general statement; one counterexample can disprove it.
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Answer: