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Lesson 2-2 Conditional Statements
89
Objectives To recognize conditional statements and their parts
To write converses, inverses, and contrapositives of conditionals
2-2
Conditional Statements
Key Concept Conditional Statements
Definition
A conditional is an if-then statement.
The hypothesis is the part p following if .
The
conclusion
is the part q following then .
Symbols
p P q
Read as
“if p then q ” or
“ p implies q .”
Diagram
q
p
The company that prints the bumper sticker at the left below
accidentally reworded the original statement and printed the sticker
three different ways. Suppose the original bumper sticker is true. Are
the other bumper stickers true or false? Explain.
The study of if-then statements and their truth values is a foundation of reasoning.
Essential Understanding
You can describe some mathematical relationships
using a variety of if-then statements.
The Venn diagram above illustrates how the set of things that satisfy the hypothesis lies
inside the set of things that satisfy the conclusion.
Dynamic Activity
Conditional
Statements
A
C
T
I
V I T
I
E
S
D
C
A
C
A
C
I
E
S
D
Y
N
A M
I
C
Lesson
Vocabulary
t! conditional
t! hypothesis
t! conclusion
t! truth value
t! negation
t! converse
t! inverse
t! contrapositive
t! equivalent
statements
L
V
L
V
t! c
L L
V V V
t c
Try to make sense
of the statements
on the bumper
stickers by
figuring out when
they are true, and
when they are
false.
Content Standards
Prepares for G.CO.9 Prove theorems about lines and
angles.
Prepares for G.CO.10 Prove theorems about triangles.
Prepares for G.CO.11 Prove theorems about
parallelograms.
MATHEMATICAL
PRACTICES

Problem 1
Got It?
Problem 2
Got It?
Problem 3
Got It?
90
Chapter 2 Reasoning and Proof
G
What would a Venn
diagram look like?
A robin is a kind of bird,
so the set of robins (R)
should be inside the set
of birds (B).
R
B
Identifying the Hypothesis and the Conclusion
What are the hypothesis and the conclusion of the conditional?
If an animal is a robin, then the animal is a bird.
Hypothesis ( p ): An animal is a robin.
Conclusion ( q ): The animal is a bird.