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2­3 Deductive Reasoning with Monty Python 2011 September 19, 2011 2­3 Deductive Reasoning Logic and Monty Python's Quest for the Holy Grail Objective: Use the law of detachment and the law of syllogism. Sep 14­10:17 AM 1 2­3 Deductive Reasoning with Monty Python 2011 weighs as much as a duck September 19, 2011 witches Write a conditional to describe the above Venn diagram. If she is a witch, then she weighs as much as a duck! Sep 14­10:29 AM 2 2­3 Deductive Reasoning with Monty Python 2011 September 19, 2011 If I give you this conditional If she is a witch, then she weighs as much as a duck! AND tell you that someone is a witch, what is the only conclusion you can make? They weigh as much as a duck! This is called the Law of Detachment If a conditional is true and it's hypothesis is true, then the conclusion is true. Symbolic Form: If p q is a true statement and p is true, then q is true. Sep 14­10:39 AM 3 2­3 Deductive Reasoning with Monty Python 2011 September 19, 2011 For the given true statements, what can you conclude? 1. If it is made of wood, then it floats on water. My boat is made of wood. Conclusion: Using the Law of Detachment, your only conclusion is that my boat floats on water. 2. If M is the midpoint of a segment, then it divides the segment into two congruent segments. M is the midpoint of AB. Conclusion: Using the Law of Detachment, your only conclusion is that AM = MB. M divides the segment into two congruent segments. Sep 14­10:51 AM 4 2­3 Deductive Reasoning with Monty Python 2011 September 19, 2011 Here are two conditionals that we will assume true: If she is a witch, then she weighs as much as a duck. If she weighs as much as a duck, then she floats on water. What conclusion can you make from the above statements? If she is a witch, then she floats on water! This is called the LAW OF SYLLOGISM If p q and q r are true statements, then p r is a true statement. Sep 14­10:59 AM 5 2­3 Deductive Reasoning with Monty Python 2011 September 19, 2011 For the given statements, what can you conclude? 1. If a number is prime, then it does not have repeated factors. If a number does not have repeated factors, then it is not a perfect square. Conclusion: If a number is prime, then it is not a perfect square. 2. If a number is divisible by 10, then it is divisible by 5. If a number ends in 0, then it is divisible by 10. Conclusion: If a number ends is 0, then it is divisible by 5. Sep 14­11:10 AM 6 2­3 Deductive Reasoning with Monty Python 2011 September 19, 2011 HOMEWORK p. 96 # 1­15, 27­31 Sep 14­11:17 AM 7