Logical Reasoning

Counter-example

A single case that shows a general statement is false.

EnglishCounter-example
Bahasa MelayuContoh penyangkal
中文反例

How it is used

The statement "the product of two prime numbers is always odd" is false. A counter-example is 2 × 3 = 6, which is even.

This single case is enough to disprove the general claim.

Where it shows up in SPM

Counter-example is the disproving tool in Form 4 Logical Reasoning. Paper 1 may ask which value is a counter-example to a claim.

Paper 2 asks you to decide whether a general statement is true and, if not, to give a counter-example that shows it is false.

Don't confuse it with

Counter-example vs proofOne counter-example is enough to disprove a general statement, but one supporting example is never enough to prove one; proving requires a general argument.
QuantifierA quantifier such as "all" sets up the general claim; a counter-example is the single case you produce to knock that "all" claim down.

Open the chapter: Logical Reasoning →

Frequently asked questions

How many counter-examples do I need?

Just one. To disprove "every number greater than 2 is prime", the value 4 is a counter-example because 4 = 2 × 2 is not prime.

A single valid case is enough; you do not need to list several.

Can a counter-example prove a statement true?

No. A counter-example can only show a statement is false.

To argue a general statement is true you need a proper reason that covers every case, not examples; finding examples that fit never proves no exception exists.

Related terms

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