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2.5 If-Then Statements and Deductive Reasoning

2.5 If-Then Statements and Deductive Reasoning. If-Then Statement : A statement with two parts: an “if” part that contains the hypothesis and a “then” part that contains the conclusion Hypothesis : The “if” part of an if-then statement (may be an implied “if”)

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2.5 If-Then Statements and Deductive Reasoning

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  1. 2.5 If-Then Statements and Deductive Reasoning

  2. If-Then Statement: A statement with two parts: an “if” part that contains the hypothesis and a “then” part that contains the conclusion • Hypothesis: The “if” part of an if-then statement (may be an implied “if”) • Conclusion: The “then” part of an if-then statement (may be an implied “then”) • Deductive Reasoning: Deductive reasoning uses facts, definitions, accepted properties and the laws of logic to make a logical argument (may not always be correct)

  3. Law of Detachment • If the hypothesis (p) of a TRUE if-then statement is true, then the conclusion (q) is also true • p  q, then true p  true q • If you are late to class, then you will be counted tardy. • Mark is late to class. • We conclude: Mark is counted tardy

  4. Law of Syllogism • If p  q and q  r are true statements, then p  r must be true as well • If you do well on all of your homework, then you will do well on tests and quizzes. If you do well on tests and quizzes, then you will pass the class. • If you do well on all of your homework, then you will pass the class

  5. Homework: • Assignment # 2 • Page 85 • Problems 1-6 all (we will do these together in class), 7-19 all, 29-43 odds only (on your own) • If you are quiet and work until you are dismissed, you will not have to write the problems on 1-19

  6. Adjacent angles share a common side.

  7. You will be late to school if you miss the bus

  8. If the endpoints of a segment have the coordinates (-1, -2) an (5,2), then the midpoint is at (2,0). • The endpoints of AB are at (-1, -2) an (5,2).

  9. If the perimeter of a square is 20 ft, then the length of a side of a square is 5ft. • If the length of a side of a square is 5 ft, then the area is 25 square ft.

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