Core Studies 5: Experimental Section

The Internet - Number Theory - Programming

Using a Counterexample to Disprove a Hypothesis

Sometimes we are given a hypothesis that we think is false. In order to prove that it is false, we can find a case for which the premises of the hypothesis are true, but the conclusion is not.

Example

Consider the following statement:
All even numbers are divisible by 4.

To disprove this statement, we must find an even number that is not divisible by 4. We might choose the number 10. Since 10 is even, but 10 is not divisible by 4, we have found a counterexample to the original hypothesis, and thus the hypothesis must be false.

Question: Could we choose the number 9 as a counterexample to the hypothesis above? Think about it before you look at the answer.

Exercise

Find counterexamples to the following statements:
  1. Every odd number is divisible by 5.
  2. Every student must take Core 5.
  3. All mammals give birth to live young.
Do them on your own first, before peeking at the answers.
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