1. Lesson 21 LAW OF DETACHMENT AND SYLLOGISM

2. Review and New Vocabulary Inductive reasoning is the process of reasoning that a rule or statement is true because specific cases are true. In other words, observing a pattern Example: Kari noticed it had rained the past four mornings. What statement might Kari make about tomorrow morning? Kari states that tomorrow it will rain in the morning. Deductive reasoning is the process of using logic to draw conclusions from given facts, definitions, properties, theorems, etc. Example: All of Martha’s children have blue eyes. Blaine is Martha’s son. What statement might be made about Blaine? Therefore, Blaine has blue eyes.

3. Use Deductive Reasoning to form a “Therefore” concluding statement a)Simone wears blue and red on game days. Today is game day. Therefore, Simone is wearing blue and red. b)To check out a book from the library, you must have a library card. Alex checked a book from the library. Therefore, Alex has a library card. c)All the chess team members won their opening match in the last tournament. Skyler is on the chess team. Therefore, Skyler won his opening match in the last tournament.

4. Forms of Deductive Reasoning LAW OF DETACHMENT For two statements p and q, when “If p, then q ” is a true statement and p is true, then q is true. LAW OF SYLLOGISM When “If p, then q ” and “If q, then r ” are true statements, then “If p, then r ” is a true statement.

5. Examples of Detachment and Syllogism LAW OF DETACHMENT If it is Monday, then Connor will go to school. Today is Monday. Therefore, Connor will go to school. LAW OF SYLLOGISM If there is a power outage, then the freezer will not work. If the freezer does not work, then the ice cream will melt. If there is a power outage, then the ice cream will melt.

6. Use Law of Detachment a)If there is a power outage, then the ice cream will melt. The power is out. Therefore, the ice cream will melt. b)If a number is greater than zero, then it is positive. Five is greater than zero. Therefore, five is a positive number. c)I get paid every Friday. Today is Friday. Therefore, I get paid today.

7. Use Law of Syllogism a)If the wind blows from the north, then the temperature drops. If the temperature drops, then Carman will need to wear a jacket. If the wind blows from the north, then Carman will need to wear a jacket. b)If the basketball team practices hard this week, then they will win the game. If the team wins the game, then they will qualify for the playoffs. If the team qualifies for the playoffs, then other teams will want the coach. If other teams want the coach, then the coach will get a raise. If the basketball team practices hard this week, then the coach will get a raise.

8. Conclusion The use of these laws will be vital when doing proofs. However you need to be careful when using deductive reasoning. Deductive reasoning may lead to a faulty conclusion, because if there is an incorrect statement or conclusion, all other conclusions are unreliable. This is why we must draw conclusions based on the information given. Do not make assumptions that are not logically sound or which have not been stated in the question.