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Lesson 2.3 p. 87 Deductive Reasoning Goals: to use symbolic notation to apply the laws of logic

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Symbolic Notation Conditional Statements Hypothesis “p”Conclusion “q” p Example: If today is Monday, then there is school. q

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Symbolic Notation Conditional Statement: If p, then qorp q Biconditional : If p q and if q p or p q p if and only if q Converse: If q, then porq p If today is Monday, then there is school. If there is school, then today is Monday. Today is Monday, if and only if there is school.

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More Symbolic Notation

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Example Converse or q p: Conditional Statement or p q: Tim will buy a car if he finds a summer job. Inverse or Contrapositive or q: p:

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Deductive Reasoning vs. Inductive Reasoning Inductive Reasoning: Uses previous examples Uses patterns Can make an educated guess Example: Kate lost her instrument. The only instrument Kate plays is the clarinet. Kate lost her clarinet. Deductive Reasoning: Uses facts Uses definitions Can prove or make a logical argument Example: It rained for the last two days, so it will rain today.

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Two Laws of Deductive Reasoning 2)Law of Syllogism: If p q and q r are true conditional statements, then p r is true. 1) Law of Detachment: If p q is a true conditional statement and p is true, then q is true. Example: Jamal knows that if he misses practice the day before a game, then he will not be able to pitch. Jamal misses practice on Tuesday. Jamal will not be able to pitch in the game on Wednesday. Example: If it is Friday, then tomorrow is Saturday. If it is Saturday, then we will go swimming. If it is Friday, then tomorrow we will go swimming.

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Examples of Laws of Deductive Reasoning 2)Law of Syllogism: If p q and q r are true condition statements, then p r is true. 1) Law of Detachment: If p q is a true condition statement and p is true, then q is true. Example: If two angles form a linear pair, then they are supplementary. Angles A and B are supplementary. Conclusion, or can it not be reached? Example: If I break my leg, then I can’t ice skate. If I can’t ice skate, I won’t go to the ice skating party. Conclusion:

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Example A foot is a measurement of twelve inches. If-then form: Converse: Inverse: Contrapositive:

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