Counterexample Math Example 4

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Example 4

easy
Find a counterexample to disprove: 'If an integer is divisible by 6, then it is divisible by 4.'

Solution

  1. 1
    Choose an integer divisible by 6, such as 6 or 12. Then test divisibility by 4.
  2. 2
    The number 6 is divisible by 6 but not by 4, so it disproves the statement.

Answer

66 is a counterexample.
A single example that satisfies the hypothesis but fails the conclusion is enough to disprove a universal or conditional claim. No further examples are needed once one counterexample is found.

About Counterexample

A counterexample is a specific instance that satisfies the hypothesis of a claim but contradicts its conclusion, thereby disproving the general statement.

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More Counterexample Examples

Example 1 easy

Disprove: 'All prime numbers are odd.'

Example 2 medium

Disprove: 'For all real numbers [formula], [formula].'

Example 3 easy

Find a counterexample to disprove: 'The sum of any two prime numbers is even.'

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