1. Chapter 2: Deductive Reasoning

2. -The process of reasoning from one or more general statements to reach a logically certain conclusion

3. Example of Deductive Reasoning https://www.youtube.com/watch?v=wYlVBhw fvL4 https://www.youtube.com/watch?v=wYlVBhw fvL4

4. 2-1: If-then Statements; Converses If-then Statements/ Conditional Statements/ Conditionals (all same thing) If p, then q Hypothesis, conclusion

5. Examples 1.) If it rains after School, I will give you a ride home.

6. Examples 1.) If it rains after School, I will give you a ride home. 2.) If B is between A and C, then AB + BC = AC

7. Examples 1.) If it rains after School, I will give you a ride home. 2.) If B is between A and C, then AB + BC = AC 3.) If I got 100% on my test, then I got an A.

8. Examples 1.) If it rains after School, I will give you a ride home. 2.) If B is between A and C, then AB + BC = AC 3.) If I got 100% on my test, then I got an A. Are either True or False

9. Examples 1.) If it rains after School, I will give you a ride home. 2.) If B is between A and C, then AB + BC = AC 3.) If I got 100% on my test, then I got an A. Are either True or False – If False, provide a counterexample If only false once, then the whole statement is still false

10. Example: If a # is a rational #, it is an integer

11. – False: ¾ – There are many true examples, but all you need is one false to make it false

12. Example: If a # is a rational #, it is an integer – False: ¾ – There are many true examples, but all you need is one false to make it false Example: If a is positive, then a > -b

13. Example: If a # is a rational #, it is an integer – False: ¾ – There are many true examples, but all you need is one false to make it false Example: If a is positive, then a > -b – False: a = 3, b = -4

14. Converse -interchanging the hypothesis and conclusion -If q, then p

15. Converse -interchanging the hypothesis and conclusion -If q, then p Converse of previous examples 1.) If I gave you a ride after school, then it rained 2.) IF AB + BC = AC, then B is between A and C 3.) If I got an A on the test, then I got 100%.

16. If 4x = 20, then x = 5. Is the converse true?

17. Biconditional If statement and converse are both true,, then it is called a biconditional – You can then use the words if and only if (iff) – 4x = 20 if and only if x = 5

18. Biconditional If statement and converse are both true, then it is called a biconditional – You can then use the words if and only if (iff) – 4x = 20 if and only if x = 5 Every definition can be written as a biconditional – Ex: Congrent segments are segments that have equal lengths – Converse: Segements that have equal lengths are congruent segments

19. Your Turn Come up with 3 examples 1.True conditional, false converse 2.False conditional 3.Biconditional

20. Other ways to write conditionals If p, then q P implies q P only if q q if p All the same thing!

22. Classwork Pg 34: 1, 4, 8, 10, 14

23. Homework: Pg 35: 1-31 odd