# Deductive Reasoning Inductive reasoning a type of reasoning

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Deductive Reasoning

Inductive reasoning - a type of reasoning that allows you to reach conclusions based on a pattern of specific examples or past events.

Use inductive reasoning to find the next two terms of the pattern § 1. 17, 23, 29, 35, 41, … § answer: 47 § 2. 1. 01, 1. 0001, … § answer: 1. 00001 § 3. Monday, Tuesday, … § answer: Wednesday § 4. December, November, … § answer: October

Deductive reasoning (or logical reasoning) is the process of reasoning logically from given statements to a conclusion. If the given statements are true, deductive reasoning produces a true conclusion.

If it is a witch, then it is made of wood. If it is made of wood, then it floats. Conclusion: If it is a witch, then it floats.

If it is made of wood, then it floats. What we know: A witch is made of wood. Therefore, it floats.

Law of Detachment § If a conditional is true and its hypothesis is true, then its conclusion is true: § If p q is a true statement and p is true, then q is true.

§ If it is made of wood, then it floats. p (true statement) A pencil is made of wood. Therefore p ___________ q q

§ If you score between 90 and 100, you will receive an A. (true statement) p Andrea scored 93. Therefore ___________ p q q

§ If you score between 90 and 100, you will receive an A. (true statement) p Audrey scored 78. Therefore ___________ q

§ If you are a Lancer, your school colors are black and gold. p statement) (true q Jerald’s school colors are black and gold. q Therefore ___________ ? ?

Law of Syllogism § If p q p r. and q r are true statements, then

If it is a witch, then it is made of wood. p q If it is made of wood, then it floats. q r Conclusion: If it is a witch, then it floats. p r

If you play tennis, you will get good exercise. p q If you get good exercise, you can keep your heart healthy. q r Conclusion: If you play tennis, _____ p r

If you are in this building, then you are in Lafayette. q r If you are in this room (room 247), then you are in this building. p p Conclusion: r q

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