It is about Conditional Statements or If-Then Statements as well as identifying if the statement is valid or invalid.

1. HYPOTHESIS AND
CONCLUSION OF
IF - THEN STATEMENTS
Module 6

2. OBJECTIVES
• determine the relationship between the hypothesis and
the conclusion of an if-then statement. M8AL-IIg-34
• transform a statement into an equivalent if-then
statement. M8GE-IIg-35

3. Definition of Terms
HYPOTHESIS (p)– is the condition in a given
statement.
CONCLUSION (q) – is the judgment reached
by reasoning.
PROPORTION – is the equality of two ratios.

4. A person, who loves to cook, makes
delicious food.
HYPOTHESIS: A person who loves to
cook
CONCLUSION: makes delicious food

5. A triangle has three vertices.
HYPOTHESIS: A triangle
CONCLUSION: has three vertices

6. How do we identify if a statement is
valid or invalid?
Hypothesis : Conclusion =
Hypothesis : Conclusion

7. Young actresses are health conscious. Norma
and Perla are young actresses, then they are
health conscious.
Conclusion: health conscious (HC)
Hypothesis: young actresses (YA)
Proportion
YA : HC = YA : HC (VALID)

8. Students who are good in Mathematics are
smart. Maria and Rowena are smart, then
they are good in Mathematics.
Conclusion: smart (S)
Hypothesis: good in Mathematics (GM)
Proportion
GM: S = S : GM (INVALID)

9. A right angle has a measure of 90°. ∠𝑨𝑩𝑪
is a right angle, therefore 𝐦∠𝑨𝑩𝑪 = 𝟗𝟎.
Conclusion: has a measure of 90°
(M)
Hypothesis: right angle (RA)
Proportion
RA: M = RA : M (VALID)

10. Marikina City is a safe environment to
live in. Pedro lives in a safe
environment, then he is in Marikina
City.
VALID OR INVALID?

11. Residents in Marikina are disciplined.
Juan and Maria live in Marikina
Heights, so they are disciplined
VALID OR INVALID?

12. Determine if the statement is valid or invalid
1.Hospitals in Marikina are clean. St. Lukes
Medical Center is clean, therefore it is
located in Marikina.
2. Vertical lines are not function. Line m is
parallel to y – axis, therefore it is not a
function.

13. Determine if the statement is valid or invalid
3. Planets revolve around the sun. Earth is a planet,
therefore it revolves around the sun.
4. Flowers are used to surprise a loved one. Sophia
was surprised by her friend, then she got flowers.
5. Southeast Asian countries are nice to visit for a
vacation. Philippines is in Southeast Asia, so it a nice
place for a vacation.

14. also called as CONDITIONAL
STATEMENTS.
IF – THEN STATEMENTS

15. Transforming a statement
into an equivalent if-then
statement

16. A. People who are happy and contented live peacefully.
Concepcion and Lourdes live peacefully, therefore they
are happy and contented.
B. Cats love to sleep. Grey is a cat, so he loves to sleep.
REVIEW

17. The word “if” signals the condition or
the hypothesis while the term “then”
states the outcome or the conclusion.
IF – THEN STATEMENTS

18. To make an if-then form, we must
follow this format:
If (hypothesis), then (conclusion).
If p, then q.
𝒑 → 𝒒
IF – THEN STATEMENTS

19. Cigarette smoking is
dangerous to your health.
Conclusion: His health is in danger.
Hypothesis: A person smokes.
If-Then form:
If a person smokes, then his health
is in danger.

20. Ana is smart because she is
studying everyday.
Conclusion: she is smart
Hypothesis: Ana is studying everyday
If-Then form:
If Ana is studying everyday, then
she is smart.

21. A segment has
exactly 1 midpoint.
Conclusion: It has exactly 1 midpoint.
Hypothesis: AB is a segment.
If-Then form:
If AB is a segment, then it has
exactly 1 midpoint.

22. A triangle consists of 3
sides, angles, and vertices.
Conclusion: It has 3 sides, angles,
and vertices.
Hypothesis: A polygon is a triangle.
If-Then form:
If a polygon is a triangle, then it has 3
sides, angles, and vertices.

23. A number is divisible by 10
if its last digit is a 0.
Conclusion: It is divisible by 10
Hypothesis: The last digit of a
number is 0
If-Then form:
If the last digit of a number is 0, then
it is divisible by 10.

24. Parallel lines do not
intersect.
Conclusion: they do not intersect.
Hypothesis: Lines are parallel
If-Then form:
If lines are parallel, then they do not
intersect.

25. Right angles are congruent.
Conclusion: they are congruent.
Hypothesis: Two angles are right
If-Then form:
If two angles are right, then they are
congruent.

26. Write the following in if-then
statements:
1. All squares are rectangle.
2. A polygon with nine sides is a
nonagon.
3. Collinear points lie on the
same line.

27. DERIVED CONDITIONAL
STATEMENTS:
Converse, Inverse and
Contrapositive
Module 7

28. OBJECTIVES
• determine the inverse, converse, and contrapositive of
an if then statement. M8GE-IIh-36

29. SIMPLE STATEMENTS
• convey only one idea.
Examples
p: The sun rises in the east.
q: 2 + 5 =7
r: 25 + x = 10 for some real number x
s: COVID 19 is a virus

30. COMPOUND STATEMENTS
• have two or more ideas.
• They can be formed in two ways; first by
negation and secondly, by using
connectives.

31. COMPOUND STATEMENTS
NEGATION
a statement whose truth
value is the opposite of the
given statement.
Symbol: ~
p: 11 is an odd number
~p: 11 is an even number
CONNECTIVES
a word or phrase that links
clauses or sentences.
1. Conjunction – and (Λ)
2. Disjunction – or (V)
3. Implication – If-then (→)

32. NEGATION

33. Write the negation of each of the
following statements
∠A is not congruent to ∠B.
Negation:
∠A is congruent to ∠B.

34. Write the negation of each of the
following statements
Diagonals bisects each other.
Negation:
Diagonals do not bisect each
other.

35. CONNECTIVES
1. Conjunction is formed when two
simple statements are joined by the
word “and” The symbol “Λ” is used to
represent the word “and”. (p^𝑞)

36. CONNECTIVES
2. Disjunction is formed when two
simple statements are joined by the
word “or” The symbol “V” is used to
represent the word “or”. (p ∨ 𝑞)

37. CONNECTIVES
3. Implication is a conditional
statement in If - then form. The
implication “ If p, then q” in symbols, (
𝐩 → 𝐪) is also read as “p implies q”
and “p is sufficient for q.” and “q is
necessary for p”.

38. DERIVED STATEMENTS
interchange negate interchange
negate

39. EXAMPLE
1.p: It is raining q: It is colder
Conditional ( 𝑝 → 𝑞 ):
If it is raining, then it is colder.

40. EXAMPLE
1.p: It is raining q: It is colder
Conditional ( 𝑝 → 𝑞 ):
If it is raining, then it is colder.
Converse ( 𝑞 → 𝑝):
If it is colder, then it is raining.

41. EXAMPLE
1.p: It is raining q: It is colder
Conditional ( 𝑝 → 𝑞 ):
If it is raining, then it is colder.
Inverse (−𝑝 → −𝑞 ):
If it is not raining, then it is not colder.

42. EXAMPLE
1.p: It is raining q: It is colder
Conditional ( 𝑝 → 𝑞 ):
If it is raining, then it is colder.
Contrapositive (−𝑞 → −𝑝 ):
If it not colder, then it is not raining.

43. 2. A quadrilateral has four
sides.
p: A polygon is a quadrilateral
q: It has four sides
Conditional ( 𝑝 → 𝑞 ):
If a polygon is a quadrilateral, then it has four
sides.
Converse ( 𝑞 → 𝑝):
If a polygon has four sides, then it is a quadrilateral.

44. A quadrilateral has four sides.
p: A polygon is a quadrilateral
q: It has four sides
Conditional ( 𝑝 → 𝑞 ):
If a polygon is a quadrilateral, then it has four
sides.
Inverse (−𝑝 → −𝑞 ):
If a polygon is not a quadrilateral, then it has no four
sides.

45. A quadrilateral has four sides.
p: A polygon is a quadrilateral
q: It has four sides
Conditional ( 𝑝 → 𝑞 ):
If a polygon is a quadrilateral, then it has four
sides.
Contrapositive (−𝑞 → −𝑝 ):
If a polygon has no four sides, then it is not a
quadrilateral.

46. Write the kind of derived statement.
Conditional statement: If it’s a right angle, then its
measure is 90 degrees.
_________1. If the measure of the angle is 90 degrees, then it is a
right angle.
_________2. If the measure of the angle is not 90 degrees, then it
is not a right angle.
_________3. If the angle is not a right angle, then its measure is
not 90 degrees

47. Write the kind of derived statement.
Conditional statement: If you do your homework,
then you will pass in Mathematics.
_________4. If you do not pass in Mathematics, then
you do not do your homework.
_________5. If you passed in Mathematics, then you
did your homework.
_________6. If you do not do your homework, then
you will not pass in Mathematics.

48. Using p and q below, write the symbolic statement in
words. Assume that p and q are true.
p: the value of x is 4
q: 3x + 2 = 14
7.p →q
8. ~p → ~q
9. q → p
10. ~q → ~p

49. 11. Converse: If two lines do not intersect, then they are
perpendicular.
Conditional: ____________________________________
Write the conditional statement.

50. 12. Inverse: If two angles have the sum of 180°, then they
are supplementary angles.
Conditional: ____________________________________
Write the conditional statement.

51. 13. Contrapositive: If two angles are not supplementary,
then their sum is not 180°.
Conditional: ____________________________________
Write the conditional statement.

52. 14. Inverse: If two lines are perpendicular, then they
intersect.
Conditional: ____________________________________
Write the conditional statement.

53. EQUIVALENCE OF TWO
STATEMENTS
Module 8

54. Using p and q below, write the symbolic statement in
words. Assume that p and q are true.
p: the value of x is 4
q: 3x + 2 = 14
1.p →q
2. ~p → ~q
3. q → p
4. ~q → ~p

55. Equivalent statements
1. Conditional and Contrapositive
2. Converse and Inverse

56. 5. Converse: If two lines do not intersect, then they are
perpendicular.
Conditional: ____________________________________
Write the conditional statement.

57. 6. Inverse: If two angles have the sum of 180°, then they
are supplementary angles.
Conditional: ____________________________________
Write the conditional statement.

58. 7. Contrapositive: If two angles are not supplementary,
then their sum is not 180°.
Conditional: ____________________________________
Write the conditional statement.

59. 8. Inverse: If two lines are perpendicular, then they
intersect.
Conditional: ____________________________________
Write the conditional statement.

60. 1. Given the symbolic pattern ~q → ~p, find its
contrapositive.

61. 2. Given the symbolic pattern p → ~q, find its
converse.

62. Try this!
What is the contrapositive of the inverse of
a conditional statement?

63. Try this!
What is the negation of the inverse of a
conditional statement?

64. Give a possible equivalent
statement.
If all the sides of a quadrilateral are not
equal, then it is not a square.

65. A. Write in symbols.
1. Converse of q -> p
2. Contrapositive of ~p -> ~ q
3. Contrapositive of ~ q -> ~ p
4. Inverse of ~ p -> ~ q

66. A. Write in symbols.
5. Inverse of p -> q
6. Inverse of ~ q -> ~ p
7. Converse of p -> q
8. Contrapositive of q -> p

67. B. Write an equivalent statement.
1. If an animal is a bat, then it is a
mammal.
2. If two lines do not intersect, then
they don’t have any common
points.

68. B. Write an equivalent statement.
3. If a number is not divisible by
two, then it is odd.
4. If the measurement of an angle
is between 0° and 90°, then it is
not acute.

71. Try this!
What is the converse of the contrapositive
of a conditional statement?

72. Try this!
What is the inverse of the converse of a
conditional statement?

73. PERFORMANCE TASK
Goal: To help your classmates and yourself to come
up with a decision to enroll in online learning or in
modular mode of learning?
Role: Advocate of continuing education despite of
pandemic.
Audience: classmates, parents

74. PERFORMANCE TASK
Goal: To help your classmates and yourself to come up with a decision to enroll in online
learning or in modular mode of learning
Role: Advocate of continuing education despite of pandemic.
Audience: classmates, parents
Situation: Classes in the “new normal” will use blended learning system where the
students will have to choose to enroll in online classes or in modular mode of learning
Product /Performance: Construct a table of advantages and disadvantages of online
class and modular mode in a short bond paper. Solicit suggestions/ advises of
advantages and disadvantages from your classmates, parents or former teachers and list
down on the table. Discuss the list with your classmates and parents then come up with
your final decision.

75. PERFORMANCE TASK
Note: The suggestions and advises must be written in If-then form with the
derived converse, inverse and contrapositive of each advantages and
disadvantages. Have a list of at least 3 suggestions or advices
Success Standard: A decision which is suitable in your living standard,
practical, safe, and will maximize your time and effort in studying your
lesson.

76. PERFORMANCE TASK
Situation: Classes in the “new normal” will use
blended learning system where the students will
have to choose to enroll in online classes or in
modular mode of learning

77. PERFORMANCE TASK
Product /Performance: Construct a table of advantages
and disadvantages of online class and modular mode in a
short bond paper. Solicit suggestions/ advises of
advantages and disadvantages from your classmates,
parents or former teachers and list down on the table.
Discuss the list with your classmates and parents then
come up with your final decision.

78. PERFORMANCE TASK
Note: The suggestions and advises must be written
in If-then form with the derived converse, inverse
and contrapositive of each advantages and
disadvantages. Have a list of at least 3 suggestions
or advices

79. PERFORMANCE TASK
Success Standard: A decision which is suitable in
your living standard, practical, safe, and will
maximize your time and effort in studying your
lesson.

80. PERFORMANCE TASK
Completeness

81. PERFORMANCE TASK