Inductive Reasoning

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Inductive Reasoning

• Lesson 3.6
• Pre-AP Geometry

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Objective

• Understand and use inductive reasoning.

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Definition Inductive Reasoning

• Inductive reasoning is he process of making
  inferences based upon observed patterns, or
  simple repetition.
• Inductive reasoning is often used in reference
  to predictions about will happen or does happen,
  based upon what has happened.
• Inductive reasoning is also called Generalizing
  as it takes specific instances and creates a
  general rule.
• (inference the forming of a conclusion from
  premises by logical methods)

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Inductive Reasoning

• Inductive reasoning, or induction, is reasoning
  from a specific case or cases and deriving a
  general rule. It draws inferences from
  observations in order to make generalizations.
• Inference can be done in four stages
• 1. Observation collect facts, without bias.
• 2. Analysis classify the facts, identifying
  patterns of regularity.
• 3. Inference From the patterns, infer
  generalizations about the relations between the
  facts.
• 4. Confirmation Testing the inference
  through further observation.

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Inductive Reasoning

• Inductive arguments can include
• Part-to-whole where the whole is assumed to be
  like individual parts (only bigger).
• Extrapolations where areas beyond the area of
  study are assumed to be like the studied area.
• Predictions where the future is assumed to be
  like the past.

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Examples Inductive Reasoning

• Maria has given Julian a present on each of his
  birthdays. Julian reasons that she will give him
  a present on his next birthday.
• Joshua has gotten a sunburn every time he has
  gone fishing. He reasons that he will get a
  sunburn the next time he goes fishing.

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Deductive Reasoning vs. Inductive Reasoning

• Deductive reasoning is based on accepted
  statements such as definitions, postulates,
  proven theorems, corollaries, and given
  information.
• Inductive reasoning is based on observation of
  patterns of past events.

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Conclusions

• A conclusion based on deductive reasoning must
  be true if hypotheses are true.
• A conclusion based on inductive reasoning is
  probably true, but not necessarily true.

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Written Exercises

• Problem Set 3.6, p. 107 3, 5, 8, 12, 15, 16
  22, 23 29 (odd)