1. Section 2.1 Conditional Statements

2. Conditional Statement A sentence in if-then form. “If” part – hypothesis “Then” part – conclusion

3. Example If you are at school, then it is a weekday. If P, then Q.

4. Example Rewrite as a conditional. a. Two points are collinear if they lie of the same line. b. All sharks have boneless skeletons. c. A number divisible by 9 is also divisible by 3. a. If two points are collinear, c. If a number is divisible by 9, b. If it is a shark, then they lie in the same line. then it has a boneless skeleton. then it is divisible by 3.

5. Counterexample An example that shows a conditional statement is false.

6. Example Find a counterexample. If a number is odd, then it is divisible by 3. 5, 7, etc. are odd numbers, but not divisible by 3. (Need only one)

7. Converse Formed by switching the hypothesis and conclusion. If Q, then P. If it is raining, then it is cloudy. PQ Conditional: If it is cloudy, then it is raining.

8. Inverse Formed by negating the hypothesis and conclusion. If it is raining, then it is cloudy. PQ Conditional: If not P, then not Q. If it is not raining, then it is not cloudy.

9. Contrapositive Formed by switching and negating the hypothesis and conclusion. If it is raining, then it is cloudy. PQ Conditional: If not Q, then not P. If it is not cloudy, then it is not raining.

10. Some Important Postulates Postulate: Through any two points there exists exactly one line. Postulate: Through any three non-collinear points there exists exactly one plane.

11. p. 75: 9-10, 14-17, 19, 22, 25-28 Homework