### 3.3 Deductive & Inductive Reasoning

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• Math Help

Inductive reasoning is the most common type of reasoning used by humans. Moreover, it is likely the only type of reasoning used by animals other than humans. For instance, a horse in a pasture might observe that "every time I touch my nose to the electric fence, it shocks me." This is a pattern that the horse has observed and, from the experiences, has formed a conclusion that touching an electric fence is unpleasant.

Although inductive reasoning is necessary and common, we should still realize that it is not infallible. Here is an example. From every observation you (and most everyone else) has made, you might conclude that all dairy calves have exactly one head.

And yet, years ago in the United States, a traveling circus had a two-headed calf on display. This unusual calf proved that the statement "all calves have exactly one head" is false. For information on this unusal phenomenon, look up "polycephaly" on the Internet.

• Consumer Suggestion

Franklin Delano Roosevelt, the 32nd President of the United States, contracted polio at the age of 39. He became an advocate for the prevention of the paralyzing disease. In 1937, FDR founded The National Foundation for Infantile Paralysis to support research and help polio victims. A comedian suggested that he call it "The March of Dimes" and have the public send in dimes for polio research. Dimes flooded the White House and research began to find a vaccine for polio. Roosevelt is now commemorated on the U.S. dime.

After the vaccine was created, March of Dimes broadened the scope of its work to prevent birth defects, premature birth, and infant death. The March for Babies walkathon is one of America's largest fundraisers with over 7 million participants.

To take part and help spread the word, visit the March of Dimes foundation.

• Checkpoint Solution

You can draw a set diagram of the inductive reasoning as follows.

• All the tigers I have seen are orange with black stripes.
• Therefore, all tigers are orange with black stripes.

Although this is valid inductive reasoning, the conclusion is not correct. Some tigers are white with black stripes. Others are pure white.

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