Unit 1: Function Families

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Unit 1: Function Families
Conditional Statements
Vocabulary
What is a statement?
• A statement is a sentence that is either
true or false, but not both.
– Example: The Atlanta Thrashers are a pro
basketball team.
– Non example: What’s your favorite music
video?
What is a conjecture?
• A conjecture is an unproven statement that
is based on observations.
What is a counterexample of a
statement?
• A counterexample is a specific case for
which a conjecture is false.
What is a conditional statement?
• A conditional statement is a logical
statement that has two parts, a hypothesis
and a conclusion.
What is “if-then” form?
• The form of a conditional statement that
uses the words “if” and “then.” The “if” part
contains the hypothesis and the “then” part
contains the conclusion.
How do you negate a statement?
• The negation of a statement is the
opposite of the original statement.
What is the converse of a statement?
• The converse of a conditional statement
switches the hypothesis and the
conclusion.
What is the inverse of a statement?
• The inverse of a conditional statement
negates the hypothesis and the
conclusion.
What is the contrapositive of a
statement?
• The contrapositive of a conditional
statement:
– First write the converse of the statement
– Then negate both the hypothesis and the
conclusion
What is a biconditional statement?
• A statement that contains the phrase “if
and only if.”
– When a statement and its converse are both
true, you can write them as a single
biconditional statement.
Write the following statement in “ifthen” form.
• An angle is an acute angle if its measure
is less than 90 degrees.
“If-then” form
• If the measure of an angle is less than 90
degrees, then it is an acute angle.
What is the hypothesis and
conclusion of the statement:
If the measure of an angle is
less than 90 degrees, then it is
an acute angle.
Write the inverse of the
statement:
If the measure of an angle is
less than 90 degrees, then it is
an acute angle.
The inverse of the statement is:
If the measure of an angle is
not less than 90 degrees, then
it is not an acute angle.
Write the converse of the
statement:
If the measure of an angle is
less than 90 degrees, then it is
an acute angle.
The converse of the statement
is:
If the angle is acute, then the
measure of the angle is less
than 90 degrees.
Write the contrapositive of the
statement:
If the measure of an angle is
less than 90 degrees, then it is
an acute angle.
The contrapositive of the
statement is:
If the angle is not acute, then
the measure of the angle is not
less than 90 degrees.
Your Turn
• Get with a partner.
• Come up with two conditional statements;
one related to mathematics and the other
with real-world context. (They may be in
“if-then” form or some other form.)
• When you have come up with these two
statements, raise your hand for me to
check and take up your statements.
Homework
• Pick another classmates paper and
complete the following types of statements
for the math and real-world statements:
– Write the converse
– Write the inverse
– Write the contrapositive
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