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Applying Deductive Reasoning Section 2.3

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Essential Question How do you construct a logical argument?

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Deductive reasoning Uses facts, accepted rules, postulates, theorems, and definitions. JUST THE FACTS!!! Inductive reasoning is based on observations.

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Logic Laws Law of Detachment: – Direct argument (if, then) – If the hypothesis is true, then the conclusion must be true. Law of Syllogism: – Chain argument (if (p q)…and (q r) …then (p r)

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Using the Law of Detachment Problems where you are asked to use the law of detachment to verify whether a statement is true will have: – A conditional statement – A given statement. – Then you will make a conclusion.

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Example If two segments BC and XY have the same length, then they are congruent. Given that you know that BC = XY. Conditional statement: If two segments BC and XY have the same length, then they are congruent. Given: You know that BC = XY The conclusion is that the segments are congruent

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Another example If Mary goes to the movies, then it is Friday or Saturday night. Mary went to the movies. Conditional statement: Given: What do we conclude is true? If Mary goes to the movies, then it is Friday Mary went to the movies. It is Friday or Saturday

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Make your own Law of Detachment Problem You will need a – conditional statement – A given statement

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Law of Syllogism These problems have 2 or more conditional statements that are combined to make a new conditional statement. You will be asked to decide what the conclusion or new conditional statement should be.

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Example Hypothesis If we follow the rules, then we will get our work done. If we get our work done, then we will do well on the test. Conclusion If follow the rules, then we will do well on the test.

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Read the hypothesis and make a conclusion If Rick takes chemistry this year, then Jesse will be Rick’s lab partner. If Jesse is Rick’s lab partner, then Rick will get an A in chemistry. If Rick takes chemistry this year, then Rick will get an A in chemistry.

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Can you think of your own syllogism problem?

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Using Inductive or Deductive reasoning Inductive reasoning, make an observation and make a conjecture based on the observation. Deductive reasoning, use definitions and facts to draw/prove a conjecture.

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Proving statements: Look for a pattern (2)(1) = 2 (2)(3) = 6 (2)(5) = 10 (2)(7) = 14 (2)(9) = 18 (2)(11) = 22 (2)(13) = 26 (2)(15) = 30 Make a conjecture An odd number times an even number is even. Prove it: Let 2n represent an even numberGiven Let m be an odd numberGiven 2n(m) = 2(n*m)Associative Property 2(n*m) is a product of 2 and a number, so it is even.

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