CONDITIONAL STATEMENTS AND ITS LOGICAL EQUIVALENCE

1. Logical Equivalence
of the
CONDITIONAL
STATEMENTs

2. illustrates the equivalences of:
(a) the conditional statement and
its contrapositive; and
(b) the converse and inverse of a
statement.
M8GE-IIg-2
LEARNING COMPETECY:

3. 1. write the statement in conditional, the
converse; the inverse; and the
contrapositive of a statement;
2. Determine the statement as true or false
3. determine logically equivalent
statements.
Objectives:

4. P R E T E S T

5. P R E T E S T

6. P R E T E S T

7. P R E T E S T

8. P R E T E S T
5. If the biconditional statement 5𝑥 − 4 = 6 𝑖𝑓 𝑎
𝑛𝑑 𝑜𝑛𝑙𝑦 𝑖𝑓 𝑥 = 2 is true, which of the following
statement/s is/are also true?
i. 𝐼𝑓 5𝑥 − 4 = 6, 𝑡ℎ𝑒𝑛 𝑥 = 2.
ii. 𝐼𝑓 𝑥 = 2, 𝑡ℎ𝑒𝑛 5𝑥 − 4 = 6.
iii. 𝐼𝑓 5𝑥 − 4 ≠ 6, 𝑡ℎ𝑒𝑛 𝑥 ≠ 2.
A. i
B. ii
C. i and ii
D. ii and iii

10. P R E T E S T
C

11. P R E T E S T
a

12. P R E T E S T
d

13. P R E T E S T
b

14. P R E T E S T
5. If the biconditional statement 5𝑥 − 4 = 6 𝑖𝑓 𝑎
𝑛𝑑 𝑜𝑛𝑙𝑦 𝑖𝑓 𝑥 = 2 is true, which of the following
statement/s is/are also true?
i. 𝐼𝑓 5𝑥 − 4 = 6, 𝑡ℎ𝑒𝑛 𝑥 = 2.
ii. 𝐼𝑓 𝑥 = 2, 𝑡ℎ𝑒𝑛 5𝑥 − 4 = 6.
iii. 𝐼𝑓 5𝑥 − 4 ≠ 6, 𝑡ℎ𝑒𝑛 𝑥 ≠ 2.
A. i
B. ii
C. i and ii
D. ii and iii
c

15. Let us use the truth
value to analyze
statement as true or
false:

16. Truth table

17. Example Direction: Tell whether the statement is TRUE
or FALSE. If false, give a counter example.
False
True
2 iseven
True
True
1. If a number is prime, then it is odd.
p: _________ q:___________ p q: ______Ex:_____
2. If you are a grade 8 student, then you are at
Junior High School.
p: _________ q:___________ p q: ______Ex:_____
3. If you are an honor student, then you are
good in math.
p: _________ q:___________ p q: ______ Ex:_____

18. Example:Direction: Tell whether the statement is TRUE
or FALSE. If false, give a counter example.
False
True
2 iseven
True
True
1. If a number is prime, then it is odd.
p: _________ q:___________ p q: ______
Example:_____
2. If you are a grade 8 student, then you are at
Junior High School.
p: _________ q:___________ p q: ______
Example:_____
False
True False
2 iseven
true
True True

19. Example:Direction: Tell whether the statement is TRUE
or FALSE. If false, give a counter example.
3. If you are an honor student, then you are
good in math.
p: _________ q:___________ p q: ______
Example:_____
False
True False
Therearesomestudentswhoaregoodinother
subjectsexceptmath,so theybecamehonor
students.

20. Let us evaluate the
four statements as
true or false:

21. Conditional (If p, then q)
If a number is even, then it
is divisible by two.
True
Converse (If q, then p)
If a number is divisible by
two, then it is even. True

22. If the Conditional and
converse both true, then it
can be written in
biconditional statement.
A number is even if and
only if it is divisible by two.
Biconditional statement: p if and only if q.

23. Inverse (If not p, then not q)
If a number is not even,
then it is not divisible by
two. True
Contrapositive (If not q, then not
p)
If a number is not divisible
by two, then it is not even.True

24. Conditional (If p, then q)
If a polygon is a square,
then it is a rectangle. True
Converse (If q, then p)
If a polygon is a rectangle,
then it is a square. False

25. Conditional (If p, then q)
If a polygon is a square,
then it is a rectangle. True
Converse (If q, then p)
If a polygon is a rectangle,
then it is a square. False
Can you rewrite the statement into
biconditional? Why?

26. Inverse (If not p, then not q)
If a polygon is not a square,
then it is a not rectangle.False
Contrapositive (If not q, then not
p)
If a polygon is not a
rectangle, then it is not a
square.
True

27. Let us determine the
four statements are
logically equivalent
statements.

28. True True
True True

29. conditional converse
If a polygon is a
square, then it is a
rectangle.
If a polygon is a
rectangle, then it is a
square.
inverse contrapositive
If a polygon is not a
square, then it is a
not rectangle.
If a polygon is not a
rectangle, then it is
not a square.
True False
False True

30. Guide Questions:
1. “Are all conditional statements
logically equivalent to its
contrapositive?”Why?
2. How about the inverse and
converse of the statements?
Why?

31. Group Activity:
Form a group of 6.
Complete the table 1 and 2.
1.Complete the 4 statements.
2.Determine the four statements as
true or false.
3.Classify the logically equivalent
statements.

32. 1
4 Forms Statement True or
False
conditional
converse If a polygon is a parallelogram, then
it is a rectangle.
inverse
contrapositive

33. 2
4 Forms Statement True or
False
conditional
converse
inverse If an animal is not a bird, then it can
not fly.
contrapositive

36. LAS#3A

37. LAS#3B

38. What have you noticed about the relationship
between the four statements?
The conditional statement is logically equivalent to
its contrapositive statement. It means that if the
conditional of the statement is true, it will follow
that the contrapositive is also true.
Let us summarize the logically equivalent
statements.

39. What have you noticed about the relationship
between the four statements?
The same with the converse and the inverse of the
statement, they are also logically equivalent. It
means that if the converse of the statement is true,
it will follow that the inverse is also true.
Let us summarize the logically equivalent
statements.

40. Application:
1.If Pedro is a Filipino, then he is hospitable.
2.If you are a Christian, then you are a Catholic.
3.If you are a Muslim, then you are Islam.
4.If you are a Lumad, then you are Indigenous
people.
5. If you are a Mangyan, then you are a Lumad.
Direction: Give the converse, inverse, and contrapositive
of the following conditional statements.
Determine the statement as true or false. Find the logical
equivalence of the statement.
4 Forms Statement True or
False
Conditional
Converse
Inverse

41. P o s t - T E S T

42. P o s t - T E S T

43. P o s t - T E S T

44. P o s t - T E S T

45. P o s t - T E S T

47. P o s t - T E S T
c

48. P o s t - T E S T
a

49. P o s t - T E S T
b

50. P o s t - T E S T
b

51. P o s t - T E S T
d

52. Thank you!!!