1. Chapter 2 Conditional Statements Where You Will Have To Learn To Think Much More Formally In Other Words Logically

2. But First Let’s Take a Brain Break

3. Objectives To understand that some mathematical relationships can be described using a variety of if-then statements. To understand that some mathematical relationships can be described using a variety of if-then statements. To recognize conditional statements. To recognize conditional statements. To write converses of conditional statements. To write converses of conditional statements.

4. Have you ever heard a person say: If you are not completely satisfied, then your money will be refunded? This is an if-then statement called a In symbols, we can write this as This means, If p then q. Conditional Statement

5. Every conditional statement has two parts. The part following the if is the HYPOTHESIS The part following the then is the CONCLUSION

6. If today is the first day of fall, then the month is September. Hypothesis:Conclusion: Example 1:Identify the Hypothesis and the Conclusion If today is the first day of Fall then the month is September

7. If you want to be fit, then get plenty of exercise. Hypothesis:Conclusion: Example 2:Identify the Hypothesis and the Conclusion

8. Example 3:Identify the Hypothesis and the Conclusion If you can see the magic in a fairy tale, you can face the future. Hypothesis:Conclusion:

9. Example 4: Write each as a conditional a. A rectangle has four right angles. b. A tiger is an animal. c. An integer that ends with 0 is divisible by 5. If a figure is a rectangle, then it has 4 right angles.

10. The ______________ of a statement interchanges the hypothesis and conclusion. In symbols, we can write this as ________. This means, if q then p.

11. Write the converse of the conditional statement. Example 5: If two lines are not parallel and do not intersect, then they are skew lines. If two lines are skew, then they are not parallel and they do not intersect.

12. Write the converse of the conditional statement Example 6: If you eat your vegetables, then you grow.

13. Write the converse of the conditional statement Example 7: If a triangle is a right triangle, then it has a 90 degree angle. If a triangle has a 90 degree angle, then it is a right triangle.

14. Truth Values (true or false?) Example 8: Write the converse of the conditional AND determine it’s truth value. If a figure is a square, then it has four sides. If a figure has four sides, then the figure is a square.

15. Truth Values (true or false?) Example 9: Write the converse of the conditional AND determine both statements’ truth value. If the statement is false give a counterexample. If two lines do not intersect, then they are parallel.

16. Truth Values (true or false?) Example 10: Write the converse of the conditional AND determine both statements’ truth value. If the statement is false give a counter example. If x = 2, then |x| = 2.

17. Truth Values (true or false?) Example 11: Write the converse of the conditional AND determine both statements’ truth value. If the statement is false give a counter example. If you travel from the United States to Kenya, then you have a passport.

18. One More Time!! A conditional statement has two parts, a hypothesis and a conclusion. When the statement is written in if-then form, the “if” part contains the hypothesis and the “then” part contains the conclusion. HYPOTHESISCONCLUSION If there are 2 points,then exactly one line exists that contains them. The converse of a conditional statement is formed by switching the hypothesis and conclusion. If exactly one line exists that contains two points,then there exists 2 points. HYPOTHESIS CONCLUSION

19. Homework Practice 2-1 Practice 2-1 Ticket Out of Class On a separate piece of paper o Write down your own conditional statement and identify the hypothesis and conclusion. o Write down the converse of your conditional statement and identify the hypothesis and conclusion. o Determine the truth value of the statements you created. if the statement is false, write a counter-example.