The document outlines conditional statements using the format 'if p, then q' to illustrate logical implications and their components, such as hypotheses and conclusions. It provides numerous examples to demonstrate how to identify and convert statements into if-then form, emphasizing the truth values of conditionals based on factual verification. Additionally, it includes exercises to practice writing statements in if-then form.

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Prepared by:
Ma. Irene G. Gonzales
Conditional Statements

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Regrets

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combination of two
statements p and q and by the
words if and then
“If p, then q.”
Ma. Irene G. Gonzales © 2015

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p: Two distinct planes intersect.
q: The intersection is a line.
Conditional:
If two distinct planes intersect,
p
then their intersection is a line.
q
Ma. Irene G. Gonzales © 2015

5. if-then statement
In symbols,
p q
read if p then q,
or p implies q
Ma. Irene G. Gonzales © 2015

6. Take note!
Conditional statements might NOT always
be written in the “if-then” form.
Examples:
I’ll wash the car if the weather is nice.
If the weather is nice, then I will wash the car.
I’ll be a millionaire when I win the lottery.
If I win the lottery, then I will be a millionaire.
Ma. Irene G. Gonzales © 2015

7. Identify the HYPOTHESIS and the CONCLUSION.
Example 1
If I win the game, then I’ll get a prize.
hypothesis
Example 2
If I say bad words, then I will be punished.
hypothesis
conclusion
conclusion
Ma. Irene G. Gonzales © 2015

8. Identify the HYPOTHESIS and the CONCLUSION.
Example 3
If I study hard, then I will graduate.
hypothesis
Example 4
I’ll bring an umbrella if it rains tomorrow.
hypothesis
conclusion
conclusion
Ma. Irene G. Gonzales © 2015

9. Identify the HYPOTHESIS and the CONCLUSION.
Example 5
I’ll wash the dishes when I’m not busy.
hypothesis
Example 6
My mom will reward me after passing the test.
hypothesis
conclusion
conclusion
Ma. Irene G. Gonzales © 2015

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Identify the HYPOTHESIS and the CONCLUSION.
Example 7
If a polygon has six sides, then it is a hexagon.
hypothesis
Example 8
If a number is even, then it is divisible by two.
hypothesis
conclusion
conclusion
Ma. Irene G. Gonzales © 2015

11. Write the following statements in if-then form.
Example 1
Cheese contains calcium.
If it is a cheese, then it contains calcium.
Example 2
Eighteen-year-olds are eligible to drive.
If you are eighteen years old, then you are
eligible to drive.
Ma. Irene G. Gonzales © 2015

12. Write the following statements in if-then form.
Example 3
Thomasians are humble.
If you are a Thomasian, then you are humble.
Example 4
A right angle measures 90 degrees.
If it is a right angle, then it measures 90 degrees.
Ma. Irene G. Gonzales © 2015

13. Write the following statements in if-then form.
Example 5
In the equation 10x = 5, x = 2.
If 10x = 5, then x = 2.
Example 6
A polygon with four sides is a quadrilateral.
If a polygon has four sides, then it is a
quadrilateral.
Ma. Irene G. Gonzales © 2015

14. Write the following statements in if-then form.
Example 7
All congruent segments have the same length.
If segments are congruent, then they have the
same length.
Example 8
All congruent angles have the same angle
measure.
If angles are congruent, then they have the same
angle measure.
Ma. Irene G. Gonzales © 2015

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Conditionals: True or False?
Conditionals can be either true or false.
A conditional is true if it can be verified by
the following:
• fact
• definition
• property
• postulate
• theorem
Ma. Irene G. Gonzales © 2015

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Conditionals: True or False?
Conditionals can be either true or false.
A false conditional occurs when:
the hypothesis is TRUE
the conclusion is FALSE
Example:
If there are three non-collinear points, then four lines
are formed.
If the sum of the angles of a polygon is 180 degrees,
then it is a square.
Ma. Irene G. Gonzales © 2015

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Try these! Drill # 1 (1/4 sheet of paper)
Write each statement in if-then form.
1. The measure of an acute angle is between 0
and 90.
2. Equilateral triangles are equiangular.
3. All whole numbers are integers.
Ma. Irene G. Gonzales © 2015

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Try these! Drill # 1 (1/4 sheet of paper)
Write each statement in if-then form.
1. The measure of an acute angle is between 0
and 90.
If an angle is acute, then its measure is
between 0 to 90.
2. Equilateral triangles are equiangular.
If triangles are equilateral, then it is
equiangular.
3. All whole numbers are integers.
If it is a whole number, then it is an integer.
Ma. Irene G. Gonzales © 2015