1. Conditional Statements
If a condition is met, then the result will occur

2. Conditional Statements
If a condition is met, then the result will occur
Hypothesis: a condition is met

3. Conditional Statements
If a condition is met, then the result will occur
Hypothesis: a condition is met (antecedent)
Conclusion: the result will occur (consequent)

4. Conditional Statements
If a condition is met, then the result will occur
Let p = a condition is met
Let q = the result will occur

5. Conditional Statements
If a condition is met, then the result will occur
Let p = a condition is met
Let q = the result will occur
If a condition is met, then the result will occur

6. Identify the hypothesis and conclusion for each of the following:

7. Identify the hypothesis and conclusion for each of the following:
If you build it, then he will come

8. Identify the hypothesis and conclusion for each of the following:
If you build it, then he will come
Hypothesis: you build it
Conclusion: he will come

9. Identify the hypothesis and conclusion for each of the following:
If the forecast is for rain, then I will take my umbrella

10. Identify the hypothesis and conclusion for each of the following:
If the forecast is for rain, then I will take my umbrella
Hypothesis: the forecast is for rain
Conclusion: I will take my umbrella

11. Identify the hypothesis and conclusion for each of the following:
If a polygon has six sides, then it is a hexagon

12. Identify the hypothesis and conclusion for each of the following:
If a polygon has six sides, then it is a hexagon
Hypothesis: a polygon has six sides
Conclusion: it is a hexagon

13. A number is divisible by 10 if its last digit is a 0
Identify the hypothesis and conclusion for each of the following, then write the statement in If…then form.
A number is divisible by 10 if its last digit is a 0

14. A number is divisible by 10 if its last digit is a 0
Identify the hypothesis and conclusion for each of the following, then write the statement in If…then form.
A number is divisible by 10 if its last digit is a 0
Hypothesis: the last digit of a number is 0
Conclusion: the number is divisible by 10

15. Identify the hypothesis and conclusion for each of the following, then write the statement in If…then form.
A number is divisible by 10 if its last digit is a 0
Hypothesis: the last digit of a number is 0
Conclusion: the number is divisible by 10
If the last digit of a number is 0, then it is divisible by 10

16. Another performance will be scheduled if the first one is sold out
Identify the hypothesis and conclusion for each of the following, then write the statement in If…then form.
Another performance will be scheduled if the first one is sold out

17. Another performance will be scheduled if the first one is sold out
Identify the hypothesis and conclusion for each of the following, then write the statement in If…then form.
Another performance will be scheduled if the first one is sold out
Hypothesis: the first performance is sold out
Conclusion: another performance will be scheduled

18. Another performance will be scheduled if the first one is sold out
Identify the hypothesis and conclusion for each of the following, then write the statement in If…then form.
Another performance will be scheduled if the first one is sold out
Hypothesis: the first performance is sold out
Conclusion: another performance will be scheduled
If the first performance is sold out, then another one will be scheduled

19. A mammal is a warm blooded animal
Identify the hypothesis and conclusion for each of the following, then write the statement in If…then form.
A mammal is a warm blooded animal

20. A mammal is a warm blooded animal
Identify the hypothesis and conclusion for each of the following, then write the statement in If…then form.
A mammal is a warm blooded animal
Hypothesis: an animal is a mammal
Conclusion: it is a warm blooded animal

21. Identify the hypothesis and conclusion for each of the following, then write the statement in If…then form.
A mammal is a warm blooded animal
Hypothesis: an animal is a mammal
Conclusion: it is a warm blooded animal
If an animal is a mammal, then it is a warm blooded animal

22. A prism with bases that are regular polygons is a regular prism
Identify the hypothesis and conclusion for each of the following, then write the statement in If…then form.
A prism with bases that are regular polygons is a regular prism

23. A prism with bases that are regular polygons is a regular prism
Identify the hypothesis and conclusion for each of the following, then write the statement in If…then form.
A prism with bases that are regular polygons is a regular prism
Hypothesis: a prism has bases that are regular polygons
Conclusion: it is a regular prism

24. A prism with bases that are regular polygons is a regular prism
Identify the hypothesis and conclusion for each of the following, then write the statement in If…then form.
A prism with bases that are regular polygons is a regular prism
Hypothesis: a prism has bases that are regular polygons
Conclusion: it is a regular prism
If a prism has bases that are regular polygons, then it is a regular prism

25. Four quarters can be exchanged for a dollar
Identify the hypothesis and conclusion for each of the following, then write the statement in If…then form.
Four quarters can be exchanged for a dollar

26. Four quarters can be exchanged for a dollar
Identify the hypothesis and conclusion for each of the following, then write the statement in If…then form.
Four quarters can be exchanged for a dollar
Hypothesis: you have four quarters
Conclusion: you can exchange them for a dollar

27. Identify the hypothesis and conclusion for each of the following, then write the statement in If…then form.
Four quarters can be exchanged for a dollar
Hypothesis: you have four quarters
Conclusion: you can exchange them for a dollar
If you have four quarters, then you can exchange them for a dollar

28. The sum of the measures of two supplementary angles is 180°
Identify the hypothesis and conclusion for each of the following, then write the statement in If…then form.
The sum of the measures of two supplementary angles is 180°

29. The sum of the measures of two supplementary angles is 180°
Identify the hypothesis and conclusion for each of the following, then write the statement in If…then form.
The sum of the measures of two supplementary angles is 180°
Hypothesis: two angles are supplementary
Conclusion: the sum of the measures of their angles is 180°

30. The sum of the measures of two supplementary angles is 180°
Identify the hypothesis and conclusion for each of the following, then write the statement in If…then form.
The sum of the measures of two supplementary angles is 180°
Hypothesis: two angles are supplementary
Conclusion: the sum of their measures is 180°
If two angles are supplementary, then the sum of their measures is 180°

31. Truth Values of Conditional Statements
Mr. Falemawl made the following statement to four of his students, Gene, Paul, Peter and Ace.
“If you do all of your homework, then you will pass this class.”

32. Truth Values of Conditional Statements
Mr. Falemawl made the following statement to four of his students, Gene, Paul, Peter and Ace.
“If you do all of your homework, then you will pass this class.”
Gene did all of his homework, and he passed the class
Paul did all of his homework, but he failed the class
Peter did not do all of his homework, but still passed the class
Ace did not do all of the homework, and he failed the class

33. “If you do all of your homework, then you will pass this class.”
To which, if any, of these students did Mr. Falemawl lie?
Gene did all of his homework, and he passed the class
Paul did all of his homework, but he failed the class
Peter did not do all of his homework, but still passed the class
Ace did not do all of the homework, and he failed the class

34. For each of these statement below, if Mr
For each of these statement below, if Mr. Falemawl lied, then put an F at the end of the statement. If Mr. Falemawl did NOT lie, then place a T at the end of the statement.
Gene did all of his homework, and he passed the class
Paul did all of his homework, but he failed the class
Peter did not do all of his homework, but still passed the class
Ace did not do all of the homework, and he failed the class

35. Let p represent the statement “did the homework” and let q represent the statement “passed the class.” Place the symbols T and F in the blanks in order to represent each of the four statements about Gene, Paul, Peter and Ace. Then determine the truth value of each statement.

36. Let p represent the statement “did the homework” and let q represent the statement “passed the class.” Place the symbols T and F in the blanks in order to represent each of the four statements about Gene, Paul, Peter and Ace. Then determine the truth value of each statement.

38. If next month is August, then this month is July
Warm Up
Identify the hypothesis and conclusion of the following statement, then write the negation of the hypothesis and the negation of the conclusion
If next month is August, then this month is July

39. If next month is August, then this month is July
Warm Up
Identify the hypothesis and conclusion of the following statement, then write the negation of the hypothesis and the negation of the conclusion
If next month is August, then this month is July
Hypothesis: next month is August
Conclusion: this month is July

40. If next month is August, then this month is July
Warm Up
If next month is August, then this month is July
Hypothesis: next month is August
Conclusion: this month is July
Negation: next month is not August
Negation: this month is not July

41. Converse, Inverse and Contrapositive

42. If next month is August, then this month is July
Find the converse, inverse and contrapositive of
If next month is August, then this month is July

43. If next month is August, then this month is July
Find the converse, inverse and contrapositive of
If next month is August, then this month is July
Converse: If this month is July, then next month is August

44. If next month is August, then this month is July
Find the converse, inverse and contrapositive of
If next month is August, then this month is July
Converse: If this month is July, then next month is August
Inverse: If next month is not August, then this month is not July

45. If next month is August, then this month is July
Find the converse, inverse and contrapositive of
If next month is August, then this month is July
Converse: If this month is July, then next month is August
Inverse: If next month is not August, then this month is not July
Contrapositive: If this month is not July, then next month is not August

46. Find the Truth Value of each statement
Statement: If next month is August, then this month is July
True
Converse: If this month is July, then next month is August
True
Inverse: If next month is not August, then this month is not July
True
Contrapositive: If this month is not July, then next month is not August
True

47. Related Conditionals
Statement
Converse
Inverse
Contrapositive

48. True If an animal is a lion, then it is a cat that can roar
Write the converse, inverse and contrapositive of the statement below. Then determine the truth value of each of the four statements
If an animal is a lion, then it is a cat that can roar
True

49. False If an animal is a lion, then it is a cat that can roar Converse
Write the converse, inverse and contrapositive of the statement below and determine the truth value of each of the four statements
If an animal is a lion, then it is a cat that can roar
Converse
If an animal is a cat that can roar, then it is a lion
False

50. False If an animal is a lion, then it is a cat that can roar Inverse
Write the converse, inverse and contrapositive of the statement below and determine the truth value of each of the four statements
If an animal is a lion, then it is a cat that can roar
Inverse
If an animal is not a lion, then it is not a cat that can roar
False

51. True If an animal is a lion, then it is a cat that can roar
Write the converse, inverse and contrapositive of the statement below and determine the truth value of each of the four statements
If an animal is a lion, then it is a cat that can roar
Contrapositive
If an animal is not a cat that can roar, then it is not a lion
True

52. Statement Converse Inverse Contrapositive
If an animal is a lion, then it is a cat that can roar
Statement
Converse
Inverse
Contrapositive

53. True If two angles have the same measure, then they are congruent
Write the converse, inverse and contrapositive of the statement below. Then determine the truth value of each of the four statements
If two angles have the same measure, then they are congruent
True

54. True If two angles have the same measure, then they are congruent
Write the converse, inverse and contrapositive of the statement below and determine the truth value of each of the four statements
If two angles have the same measure, then they are congruent
Converse
If two angles are congruent, then they have the same measure
True

55. True If two angles have the same measure, then they are congruent
Write the converse, inverse and contrapositive of the statement below and determine the truth value of each of the four statements
If two angles have the same measure, then they are congruent
Inverse
If two angles do not have the same measure, then they are not congruent
True

56. True If two angles have the same measure, then they are congruent
Write the converse, inverse and contrapositive of the statement below and determine the truth value of each of the four statements
If two angles have the same measure, then they are congruent
Contrapositive
If two angles are not congruent, then they do not have the same measure.
True

57. Statement Converse Inverse Contrapositive
If two angles have the same measure, then they are congruent
Statement
Converse
Inverse
Contrapositive

58. False If a number is divisible by 2, then it is divisible by 4
Write the converse, inverse and contrapositive of the statement below. Then determine the truth value of each of the four statements
If a number is divisible by 2, then it is divisible by 4
False

59. True If a number is divisible by 2, then it is divisible by 4 Converse
Write the converse, inverse and contrapositive of the statement below and determine the truth value of each of the four statements
If a number is divisible by 2, then it is divisible by 4
Converse
If a number is divisible by 4, then it is divisible by 2
True

60. True If a number is divisible by 2, then it is divisible by 4 Inverse
Write the converse, inverse and contrapositive of the statement below and determine the truth value of each of the four statements
If a number is divisible by 2, then it is divisible by 4
Inverse
If a number is not divisible by 2, then it is not divisible by 4
True

61. False If a number is divisible by 2, then it is divisible by 4
Write the converse, inverse and contrapositive of the statement below and determine the truth value of each of the four statements
If a number is divisible by 2, then it is divisible by 4
Contrapositive
If a number is not divisible by 4, then it is not divisible by 2.
False

62. Statement Converse Inverse Contrapositive
If two angles have the same measure, then they are congruent
Statement
Converse
Inverse
Contrapositive