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Provide a counterexample for the statement "if an animal has four legs, then it is a dog."

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connorcolin3

Posted December 15, 2011 at 1:27 AM via web

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Provide a counterexample for the statement "if an animal has four legs, then it is a dog."

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pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted December 15, 2011 at 1:40 AM (Answer #1)

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In logic, a counterexample is simply an example that proves the conclusion made in a statement to be false.  In the statement you have provided, the hypothesis is "if an animal has four legs" and the conclusion is "then it is a dog."  A counterexample would be any example that fulfills the hypothesis but is contrary to the conclusion.

In other words, any example of an animal with four legs is a counterexample to this statement if the animal is not a dog.  Of course, there are all kinds of animals with four legs that are not dogs.  Each of these animals (elephant, cheetah, horse, cow, pig) is a counterexample because it has four legs but is not a dog.

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