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Communication Complexity

11 Examples of a Counterexample

 , November 14, 2023
A counterexample is a specific example that contradicts a general statement or hypothesis. This is used to disprove statements in logic, rational thought and debate. As such, counterexamples are stronger than nonexamples that are more often used to illustrate a concept. The following are illustrative examples of a counterexample.
Hypothesis: All birds can fly

Counterexample: Penguins
Hypothesis: All triangles have equal sides.

Counterexample: Scalene triangles have sides of different lengths.
Hypothesis: All even numbers are divisible by 4.

Counterexample: 6 is an even number but is not divisible by 4.
Hypothesis: All prime numbers are odd.

Counterexample: 2 is a prime number and is even.
Hypothesis: All liquids freeze at 0 degrees Celsius.

Counterexample: The freezing point of Mercury is about -38.83 degrees Celsius.
Hypothesis: All thunderstorms produce lightning.

Counterexample: Some thunderstorms do not produce lightning.
Hypothesis: All deserts are hot.

Counterexample: Antarctica is a cold desert.
Hypothesis: All wood floats in water.

Counterexample: Ebony wood is dense and sinks in water.
Hypothesis: All fruits are sweet.

Counterexample: Lemons are fruits but are sour.
Hypothesis: All flowers are brightly colored.

Counterexample: Bat flowers are a dark color close to black.
Hypothesis: All liquids evaporate at the same rate.

Counterexample: Water evaporates faster than honey.


A counterexample is an instance that may disprove a strongly stated general rule or act as an exception to a rule that is usually true.
Next: Nonexample
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