Practice Counterexample in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A counterexample is a specific instance that satisfies the hypothesis of a claim but contradicts its conclusion, thereby disproving the general statement.
One case where it fails is enough to kill a 'for all' claim.
Example 1
easyDisprove: 'All prime numbers are odd.'
Example 2
mediumDisprove: 'For all real numbers x, x^2 > x.'
Example 3
easyFind a counterexample to disprove: 'The sum of any two prime numbers is even.'
Example 4
easyFind a counterexample to disprove: 'If an integer is divisible by 6, then it is divisible by 4.'