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Conditional
Statements
Prepared by:
Ma. Irene G. Gonzales
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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
if-then statement
In symbols,
p
q
Ma. Irene G. Gonzales © 2015
read if p then q,
or p implies q
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
Identify the HYPOTHESIS and the CONCLUSION.
Example 1
If I win the game, then I’ll get a prize.
hypothesis
conclusion
Example 2
If I say bad words, then I will be punished.
hypothesis
Ma. Irene G. Gonzales © 2015
conclusion
Identify the HYPOTHESIS and the CONCLUSION.
Example 3
If I study hard, then I will graduate.
hypothesis
conclusion
Example 4
I’ll bring an umbrella if it rains tomorrow.
conclusion
Ma. Irene G. Gonzales © 2015
hypothesis
Identify the HYPOTHESIS and the CONCLUSION.
Example 5
I’ll wash the dishes when I’m not busy.
conclusion
hypothesis
Example 6
My mom will reward me after passing the test.
conclusion
Ma. Irene G. Gonzales © 2015
hypothesis
Identify the HYPOTHESIS and the CONCLUSION.
Example 7
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If a polygon has six
sides, then it is a hexagon.
hypothesis
conclusion
Example 8
If a number is even, then it is divisible by two.
hypothesis
Ma. Irene G. Gonzales © 2015
conclusion
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
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
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
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
Conditionals: True or False?
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Conditionals can be either true or false.
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A conditional is true if it can be verified by
the following:
• fact
• definition
• property
• postulate
• theorem
Ma. Irene G. Gonzales © 2015
Conditionals: True or False?
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Conditionals can be either true or false.
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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
Try these! Drill # 1 (1/4 sheet of paper)
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Write each statement in if-then form.
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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
Try these! Drill # 1 (1/4 sheet of paper)
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Write each statement in if-then form.
1.
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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