Section 2.3 Deductive Reasoning.

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Section 2.3 Deductive Reasoning

Inductive vs. deductive Reasoning Do you remember what Inductive Reasoning is? Reasoning based on patterns you observe Deductive Reasoning (logical reasoning) Process of reasoning logically from given statements to a conclusion. In other words… INDUCTIVE REASONING uses rules to make conclusions DEDUCTIVE REASONING uses examples to make conclusions

LAW OF Detachment If a conditional is true and its hypothesis is true, then its conclusion is true. In Symbolic Form: If p  q is a true statement and p is true, then q is true. Example 1: Using the Law of Detachment If an angle is obtuse, then it cannot be acute. Angle B is obtuse. CONCLUSION: Angle B cannot be acute

LAW OF Detachment Cont… Example 2: Using the Law of Detachment If Z is the midpoint of a segment, then it divides the segment into two congruent segments. Z is the midpoint of ST CONCLUSION: Z divides ST into two congruent segments. Example 3: Using the Law of Detachment If a road is icy, then driving conditions are hazardous. Driving conditions are hazardous. CONCLUSION: Not possible; you do not know the hypothesis is true

Law of syllogism Allows you to state a conclusion from two true conditional statements when the conclusion of one statement is the hypothesis of the other statement. NOTE: This is like the Transitive Property If a = b and b = c, then a = c In Symbolic Form: If p  q and q  r are true statements, then p  r is a true statement Example 1: Using the Law of Syllogism If it is Sunday, the Mr. Z has a lot of free time. If Mr. Z has a lot of free time, then he will watch football CONCLUSION: If it is Sunday, the Mr. Z will watch football

Law of syllogism Cont… Example 2: If it is 7:30 AM, then the Libertyville high school day begins. If the Libertyville high school day begins, then Jason will report to his 1st hour class. CONCLUSION: If it is 7:30 AM, then Jason will report to his 1st hour class. Example 3: If two angles are a linear pair, then their sum is 180 degrees. If two angles are a linear pair, then they are adjacent angles. CONCLUSION: Not Possible; q  r