1. Deductive Reasoning

2. Warm-up

4. Objectives: 1) To use the Law of Detachment 2) To use the Law of Syllogism

5. Deductive Reasoning Deductive Reasoning: The process of reasoning logically from given statements to a conclusion. Many people use deductive reasoning all the time.

6. Deductive Reasoning Because you don’t know the outcome will always be true with inductive reasoning, many times we use deductive reasoning to show that something will ALWAYS be true. With deductive reasoning, we start with a general case or cases, and use these to prove a specific case…which is the opposite of inductive reasoning.

7. The Parts of Deductive Reasoning Undefined terms are things that we accept but don’t formally define. A definition uses known words to describe a new word. A postulate is a statement that we assume to be universally true. A theorem is a statement that has been proven true using definitions, postulates, or other theorems.

8. Law of Detachment

9. Using Law of Detachment What can you conclude from the given statements? 1) If a student gets an A on a final exam, then the student will pass the course. Felicia got an A on her history exam. 2) If it is snowing, then the temperature is less than or equal to 32 degrees Fahrenheit. It is 20 degrees Fahrenheit.

10. 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. Symbolic Form: If p  q and q  r are true statements, then p  r is a true statement. Example: 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:

11. Using the Law of Syllogism If a number ends in 0, then its divisible by 10. If a number is divisible by 10, then it is divisible by 5. Conclusion: If a figure is a square, then the figure is a rectangle. If a figure is a rectangle, then the figure has four sides. Conclusion:

12. Using Both Laws If a river is more than 4000 mi. long, then it is longer than the Amazon. If a river is longer than the Amazon, then it is the longest river in the world. The Nile is 4132 mi. long. What can you conclude?

13. 2.4 Homework: Mathxlforschool.com Due Sunday @ midnight.