Section 2.2 An Introduction to Logic

1. Section 2.2 An Introduction to Logic

2. Objectives: • wSWBAT define conditionals and • model them with Euler diagrams • wUse conditionals in logical arguments • wForm converses of conditionals • wCreate logical chains from • conditionals

3. All Corvette’s are Chevy’s. corvette Rewrite the statement as a conditional statement. chevy If a car is a Corvette, then it is a Chevy.

4. If a car is a corvette , then it is a chevy. Hypothesis Conclusion

5. Let's say Mr. Amsler's car is a corvette. Where would it go in the Euler diagram? Corvette Chevy

6. What if it was a chevy, but not a corvette? Corvette Chevy

7. What if he drove a Ford? Corvette Chevy

8. rectangle rhombus quadrilateral square

9. Geometry Students Students in 9th Grade Students wearing glasses

10. Conditional If it is a dog , then it is a cat. Converse If then

11. You Try! Conditional: If a triangle is equilateral, then it is isosceles. Converse: If a triangle is isosceles, then it is equilateral.

12. Logical Chains! If a, then b. If b, then c. If c, then d. If d, then e. If e, then f. If f, then g. What is your conclusion???

13. Let's try another If sirens shriek, hen mice frisk. If mice frisk, then cats freak. If cats freak, then dogs howl. Conclusion? If sirens shriek, then dogs howl.

15. If <AXB and <BXD form a linear pair <AXB and <BXD are supplementary m<BXC + m<CXD = 90 then <AXB and <BXD are supplementary. then m<AXB + m<BXD = 180 then m<AXB = 90

16. What Have We Learned to • Model conditionals using Euler diagrams • Use conditionals in logical arguments • How to write the converse of a conditional • Create logical chains from conditionals

17. Geometric Philosophy Saying: May you find success as you angle for that square deal that will land you in the eternal triangle of life where those who walk the line always get to the point.