Unit 1: Function Families

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Unit 1 Function Families

• Conditional Statements Vocabulary

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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 Whats your favorite music video?

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What is a conjecture?

• A conjecture is an unproven statement that is
  based on observations.

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What is a counterexample of a statement?

• A counterexample is a specific case for which a
  conjecture is false.

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What is a conditional statement?

• A conditional statement is a logical statement
  that has two parts, a hypothesis and a conclusion.

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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.

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How do you negate a statement?

• The negation of a statement is the opposite of
  the original statement.

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What is the converse of a statement?

• The converse of a conditional statement switches
  the hypothesis and the conclusion.

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What is the inverse of a statement?

• The inverse of a conditional statement negates
  the hypothesis and the conclusion.

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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

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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.

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Write the following statement in if-then form.

• An angle is an acute angle if its measure is less
  than 90 degrees.

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If-then form

• If the measure of an angle is less than 90
  degrees, then it is an acute angle.

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What is the hypothesis and conclusion of the
statementIf the measure of an angle is less
than 90 degrees, then it is an acute angle.
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Write the inverse of the statement If the
measure of an angle is less than 90 degrees, then
it is an acute angle.
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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.
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Write the converse of the statement If the
measure of an angle is less than 90 degrees, then
it is an acute angle.
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The converse of the statement is If the angle
is acute, then the measure of the angle is less
than 90 degrees.
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Write the contrapositive of the statement If
the measure of an angle is less than 90 degrees,
then it is an acute angle.
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The contrapositive of the statement is If the
angle is not acute, then the measure of the angle
is not less than 90 degrees.
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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.

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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