DO NOW

1. DO NOW • Take a blank notecard from the front bookshelf. • Explain why the following statements are false. • If you live in California, you live in Watts • If the ground is wet, then it has been raining.

2. Introduction to Logic Logic and Reasoning

3. Today’s Objectives • Use counterexamples to disprove conditional statements. • Explain the relationship between hypothesis and conclusion. • Find the converse, inverse, contrapositive, and biconditional statements from a conditional statement. • Use Problem Solving Skills

4. Conditional Statement • An if-then statement • Symbolized by p –> q • Which p is a hypothesis and q is a conclusion.

5. Making a statement conditional. • Get rid of the word “all” or “every.” • Replace it with “if” • Make sense of the statement (add necessary words) • Everyone who lives in Watts lives in California. • All trees are green. • Every teacher at Simon Tech is Canadian.

6. Hypothesis (p) • If you live in Watts, then you live in California. • If it has been raining, then the ground is wet.

7. Conclusion (q) • If you live in Watts, then you live in California. • If it has been raining, then the ground is wet.

8. If hypothesis, then conclusion. • If p, then q.

9. Counterexample • Proves that a conditional statement is false. • Fits the hypothesis but not the conclusion.

10. Negation • The statement the counterexample fits. • If p then not q. • If you live in Watts, then you do not live in California.

11. Converse • Reversing the hypothesis and conclusion. • If q then p. • If you live in California, then you live in Watts.

12. Inverse • Negating the hypothesis and conclusion. • If not p then not q. • If you do not live in Watts, then you do not live in California.

13. Contrapositive • Negating the hypothesis and conclusion AND reversing them. • If not q then not p. • If you do not live in California, then you do not live in Watts.

14. Biconditional • The conditional and the converse combined • If p then q AND if q then p. • P if and only if q. • P iff q. • You live in California if and only if you live in Watts.

15. On your notecard… • Write a conditional statement. (in If-then form)

16. Practice

17. Today’s Objectives • Use counterexamples to disprove conditional statements. • Explain the relationship between hypothesis and conclusion. • Find the converse, inverse, contrapositive, and biconditional statements from a conditional statement. • Use Problem Solving Skills

18. Exit slip • 1. Give a counterexample to the statement “If you are a student at Simon Tech, you live in Watts.” • 2. Explain the relationship between the hypothesis and conclusion. (You may use the statement in #1 or #3 if you would like.) • 3. If I receive a scholarship, I will go to college. • A. Write the negation. • B. Write the converse. • C. Write the inverse. • D. Write the contrapositive. • 4. Write a statement that you are a counterexample to.

19. DO NOW • Take a blank notecard from the front bookshelf (for later). • In your notebook, explain why the following statements are false. • If you live in California, you live in Watts • If the ground is wet, then it has been raining.

20. Introduction to Logic Logic and Reasoning

21. Today’s Objectives • Use counterexamples to disprove conditional statements. • Explain the relationship between hypothesis and conclusion. • Find the converse, inverse, contrapositive, and biconditional statements from a conditional statement. • Use Problem Solving Skills

22. Conditional Statement • An if-then statement • Symbolized by p –> q • Which p is a hypothesis and q is a conclusion.

23. Making a statement conditional. • Get rid of the word “all” or “every.” • Replace it with “if” • Make sense of the statement (add necessary words) • Everyone who lives in Watts lives in California. • All trees are green. • Every teacher at Simon Tech is Canadian.

24. Hypothesis (p) • If you live in Watts, then you live in California. • If it has been raining, then the ground is wet.

25. Conclusion (q) • If you live in Watts, then you live in California. • If it has been raining, then the ground is wet.

26. If hypothesis, then conclusion. • If p, then q.

27. Counterexample • Proves that a conditional statement is false. • Fits the hypothesis but not the conclusion.

28. Negation • The statement the counterexample fits. • If p then not q. • If you live in Watts, then you do not live in California.

29. Converse • Reversing the hypothesis and conclusion. • If q then p. • If you live in California, then you live in Watts.

30. Inverse • Negating the hypothesis and conclusion. • If not p then not q. • If you do not live in Watts, then you do not live in California.

31. Contrapositive • Negating the hypothesis and conclusion AND reversing them. • If not q then not p. • If you do not live in California, then you do not live in Watts.

32. Biconditional • The conditional and the converse combined • If p then q AND if q then p. • P if and only if q. • P iff q. • You live in California if and only if you live in Watts.

33. On your notecard… • Write a conditional statement. (in If-then form)

34. Practice

35. Today’s Objectives • Use counterexamples to disprove conditional statements. • Explain the relationship between hypothesis and conclusion. • Find the converse, inverse, contrapositive, and biconditional statements from a conditional statement. • Use Problem Solving Skills

36. Exit slip • 1. Give a counterexample to the statement “If you are a student at Simon Tech, you live in Watts.” • 2. Explain the relationship between the hypothesis and conclusion. (You may use the statement in #1 or #3 if you would like.) • 3. If I receive a scholarship, I will go to college. • A. Write the negation. • B. Write the converse. • C. Write the inverse. • D. Write the contrapositive. • 4. Write a statement that you are a counterexample to.

37. DO NOW • Take a blank notecard from the front bookshelf (for later). • In your notebook, explain why the following statements are false. • If you live in California, you live in Watts • If the ground is wet, then it has been raining.

38. Error Analysis • Compare your exit slip to this example.

39. Introduction to Logic Logic and Reasoning

40. Today’s Objectives • Use counterexamples to disprove conditional statements. • Explain the relationship between hypothesis and conclusion. • Find the converse, inverse, contrapositive, and biconditional statements from a conditional statement. • Use Problem Solving Skills

41. Conditional Statement • An if-then statement • Symbolized by p –> q • Which p is a hypothesis and q is a conclusion.

42. Making a statement conditional. • Get rid of the word “all” or “every.” • Replace it with “if” • Make sense of the statement (add necessary words) • Everyone who lives in Watts lives in California. • All trees are green. • Every teacher at Simon Tech is Canadian.

43. Hypothesis (p) • If you live in Watts, then you live in California. • If it has been raining, then the ground is wet.

44. Conclusion (q) • If you live in Watts, then you live in California. • If it has been raining, then the ground is wet.

45. If hypothesis, then conclusion. • If p, then q.

46. Counterexample • Proves that a conditional statement is false. • Fits the hypothesis but not the conclusion.

47. Negation • The statement the counterexample fits. • If p then not q. • If you live in Watts, then you do not live in California.

48. Converse • Reversing the hypothesis and conclusion. • If q then p. • If you live in California, then you live in Watts.

49. Inverse • Negating the hypothesis and conclusion. • If not p then not q. • If you do not live in Watts, then you do not live in California.

50. Contrapositive • Negating the hypothesis and conclusion AND reversing them. • If not q then not p. • If you do not live in California, then you do not live in Watts.