1. 2.1 CONDITIONAL STATEMENTS 10/2

2. Learning Targets I can find the truth value given a conditional and a converse I can rewrite a statement as a conditional and write the conditional’s converse.

3. If-Then Statements Ex: If you spend more time studying for the exam, then you will get a better grade. Conditional – Another name for an if-then statement; has two parts…the part following if is the hypothesis, and the part following then is the conclusion

4. If-Then Statements Ex: If you spend more time studying for the exam, then you will get a better grade. Hypothesis: you spend more time studying for the exam. Conclusion: you will get a better grade.

5. Identifying the Hypothesis and Conclustion If today is the first day of fall, then the month is September. If y – 3 = 5, then y = 8 If two lines are parallel, then the lines are coplanar.

6. Writing a Conditional You are taking a sentence and rewriting it in if-then form.

7. Writing a Conditional An integer that ends with 0 is divisible by 5. If an integer ends with 0, then it is divisible by 5

8. Practice 1) An acute angle measures less than 90 degrees. 2) A square has four congruent sides. 3) Two skew lines do not line in the same plane.

9. Truth Value Every conditional has a truth value. The truth value is either true or false. True - it has to be true all of the time. False - you need to provide just one counterexample (an example that proves a statement false).

10. Finding Counterexamples If it is February, then there are only 28 days in the month. If x² ≥ 0, then x ≥ 0.

11. Converse The converse of a conditional switches the hypothesis and conclusion. So… If THIS, then THAT becomes If THAT, then THIS

12. Writing Converses EX : Conditional: If two lines intersect to form right angles, then they are perpendicular. Converse: If two lines are perpendicular, then they intersect to form right angles.

13. You try… Conditional : If x = 9, then x + 3 = 12 Converse: __________________

14. Truth values with Converses If a conditional is true, it doesn’t necessarily mean the converse is true also. You need to be able to determine: 1) is a conditional true or false, and 2) is the converse true or false

15. Example: If a figure is a square, it has four sides. Step 1) Determine if the conditional is true or false. Yes, it is true. Step 2) write its converse. If a figure has four sides, then it is a square. Step 3) Determine the truth value. Remember, if it is false, you must provide a counterexample. False, a Rectangle

16. Try: Conditional: If x² = 25, then x = 5 Truth Value of Conditional: Converse: Truth Value of Converse:

18. Symbolic Form Conditional p  q (If p, then q) Converse q  p (if q, then p)

19. 2-1 Packet #1-13

20. Homework P. 71 #3-31 odd, 43, 45, 47