Counterexample Math Example 3

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Example 3

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

Solution

  1. 1
    Consider the primes 2 and 3: 2+3=52 + 3 = 5, which is odd.
  2. 2
    This is a counterexample since the statement claims the sum is always even.

Answer

Counterexample: 2+3=5 (odd)\text{Counterexample: } 2 + 3 = 5 \text{ (odd)}
The number 2 is the only even prime, so adding 2 to any odd prime yields an odd sum, disproving the universal claim.

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 4 easy

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

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