The document explains conditional statements, specifically if-then statements, which consist of a hypothesis and a conclusion. It details how to identify and transform these statements, as well as the related concepts of converse, inverse, and contrapositive. Several examples and exercises are provided to illustrate these concepts.

1. If-then
Statements

2. Conditional Statement
• A logical type of statement that has two parts: a
hypothesis and a conclusion. Conditional can be
written in IF-THEN form.
• A conditional statement is a compound statement
of the form “If p then q“ where p and q are
statements.

3. • The first statement, p, is called the hypothesis
and usually begins with if, while the second
statement, q, which usually begins with then is
called the conclusion.
• If HYPOTHESIS, then CONCLUSION.
• If _____________, then ______________.
Hypothesis (p) Conclusion (q)

4. Hypothesis- It states the given facts that are
assumed to be true.
Conclusion- What need to be proven or
established.
Implication- is a statement formed by hypothesis
and conclusion.
“If p, then q.” “p q”

5. Let us connect the given input and output
using the if-then form.
Input: I studied for my math test.
Output: I got a good grade.
So, using the if- then statement, the input is the hypothesis of
the statement and the output is the conclusion of the
statement.
Answer: If I studied for my math test, then I got a good
grade.

6. Let us connect the given input and output
using the if-then form.
Input: It is raining.
Output: We need to use our umbrella.
So, using the if- then statement, the input is the hypothesis of
the statement and the output is the conclusion of the
statement.
Answer: If it is raining, then we need to use our umbrella.

7. Example #1
If a number is greater than zero, then the
number is positive.
Hypothesis: The number is greater than zero.
Conclusion: The number is positive.

8. Example #2
If it’s a quadrilateral, then it has four sides.
Hypothesis: It’s a quadrilateral.
Conclusion: It has four sides.

9. Example #3
If 3(n+1) = 6, then n= 1.
Hypothesis: 3(n+1) = 6
Conclusion: n= 1

10. Example #4
Getting enough sleep is good for your health.
Hypothesis: Getting enough sleep
Conclusion: Good for your health.

11. Example #5
An integer that ends in 1,3,5,7 and 9 is an odd
integer.
Hypothesis: An integer that ends in 1,3,5,7 and 9
Conclusion: It is an odd integer

12. Example #6
All prime number are numbers with no other
factor aside from 1 and itself.
Hypothesis: Numbers with no other factor aside
from 1 and itself
Conclusion: It is a prime number

13. Example #7
You have a fever if your body temperature is above
37.6 ℃
Hypothesis: Your body temperature is above 37.6
℃
Conclusion: You have a fever.

18. Transforming a
Statement
into an
Equivalent If-
then Statement

19. You learned how to identify the hypothesis and
conclusion of a given conditional statement. But
not all conditional statements are written in if-
then form where the hypothesis-conclusion can
be easily identified. In some conditional
statements, conclusions are written before the
hypothesis.

35. Determining
the Inverse,
Converse
and
Contrapositi
ve
of an If-then

36. Every conditional statement
has three (3) related
statements and these are
converse, inverse and
contrapositive conditional.

38. Converse
To write the converse of a conditional
statement, simply interchange the
hypothesis and the conclusion. That is,
the then part becomes the if part and the
if part becomes the then part.

39. Inverse
To write the inverse of a conditional
statement, simply negate both the
hypothesis and conclusion.

40. Contrapositive
To form the contrapositive of a
conditional statement, first, get its
inverse. Then,
interchange its hypothesis and
conclusion.

43. More Examples

44. Converse

47. Biconditional Statement

49. Inverse

50. Contrapositive

51. Exercises

52. Exercises
“A guitar is a musician”

53. Logically Equivalent

56. Directions: Determine the following statement if it is
converse, inverse or contrapositive of the given
conditional (if-then) 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

57. Directions: Determine the following statement if it is
converse, inverse or contrapositive of the given
conditional (if-then) 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.

58. For items 7-10, refer to the statement
below.
“If a figure is a square, then it has 4 equal
sides.”
7. What is the hypothesis of the statement?
A. equal sides
B. is a square
C. a figure is a square
D. it has 4 equal sides

59. For items 7-10, refer to the statement
below.
“If a figure is a square, then it has 4 equal
sides.”
8. If a figure is not square, then it doesn’t have 4
equal sides.
A. contrapositive
B. converse
C. if-then
D. inverse

60. For items 7-10, refer to the statement
below.
“If a figure is a square, then it has 4 equal
sides.”
9. If a figure has 4 equal sides, then it is a
square.
A. conclusion
B. contrapositive
C. converse
D. inverse

61. For items 7-10, refer to the statement
below.
“If a figure is a square, then it has 4 equal
sides.”
10. If a figure doesn’t have 4 equal sides, then it
is not a square.
A. contrapositive C. hypothesis
B. converse D. inverse