2.3: Deductive Reasoning p. 85-91. Deductive Reasoning Use facts, definitions and accepted properties in logical order to write a logical argument.

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2.3: Deductive Reasoning p

Deductive Reasoning Use facts, definitions and accepted properties in logical order to write a logical argument.

Law of Detachment If p q is a true conditional statement and p is true, then q is true. Ex. 1)If I pass the test, then I get an A in geometry. (p q) 2)I passed the test.(p) 3)So I got an A in geometry.(q)

Law of Syllogism If p q and q r are true conditional statements, then p r is true. Ex. 1) If I pass the test, then I get an A in geometry. 2) If I get an A in geometry, then I get a new car. 3) I passed the test so I get a new car.

Ex 1. Law of Detachment or Law of Syllogism or neither 1. If an angle is acute, then it is not obtuse. 2. <ABC is acute. 3. <ABC is not obtuse. Valid by Law of Detachment

Ex 2. Law of Detachment or Law of Syllogism or neither 1. Right angles are congruent. 2. <A <B 3. <A and <B are right angles. Invalid. Statement 2 is not related to the hypothesis

Ex 3.Law of Detachment or Law of Syllogism 1. If you save a penny, then you have earned a penny. 2. Art saves a penny. 3. Art has earned a penny. Valid by Law of Detachment.

Ex 4. Law of Detachment or Law of Syllogism or neither 1. If you are a teenager, then you are always right. 2. If you are always right, then people will listen to you. 3. If you are a teenager, then people will listen to you. Valid by Law of Syllogism.

Ex 5. Law of Detachment or Law of Syllogism 1. If you drive 50 miles per hour in a school zone, then you will get a speeding ticket. 2. Pat received a speeding ticket. 3. Pat was driving 50 miles per hour in a school zone. Invalid. Pat could have received a speeding ticket for speeding on the highway.

For the following examples, write a conclusion using the true statements. If no conclusion is possible, write no conclusion. State the applicable law.

Example 1 If Jim gets stung by a bee, then he will get very ill. If he gets very ill, then he will go to the hospital. Jim gets stung by a bee. Conclusion? Jim will go to the hospital. Law of Syllogism

Example 2 If two planes intersect, then their intersection is a line. Plane T and plane W intersect. Conclusion? Plane T and plane W intersect in a line. Law of Detachment

Example 3 If you cut class, then you will receive ISS. You cut class. Conclusion? You received ISS. Law of Detachment

Example 4 If Mike doesn’t work hard, then he won’t start the game and will quit the team. Mike quit the team. Conclusion? No conclusion. We do not why he quit the team.