Warm-Up
Exercises
Bell Work
Get out your Sudoku.
Warm-Up
Exercises
Recap
• If-then or Conditional Statements
• Truth Value
Warm-Up
Exercises
Notes
• Sometimes we want to know if the “opposite” is true.
• We call the opposite the converse.
• We write the converse by switching the hypothesis and the
conclusion.
• For example:
Conditional: If I play football, then I am an athlete.
Converse: If I am an athlete, then I play football.
Warm-Up
Exercises
Notes
• Is the converse of a conditional always true?
• True = always true
• False = just need to find one counterexample
Warm-Up2Exercises
EXAMPLE
Write the converse of the conditional statement.
“If you are a guitar player, then you are a musician.”
Decide whether the conditional is true or false.
Decide whether the converse is true or false.
Warm-Up
Exercises
Notes
• We also can write the inverse.
• We write the converse by negating the hypothesis and
conclusion.
• For example:
Conditional: If I play football, then I am an athlete.
Inverse: If I do not play football, then I am not an athlete.
Warm-Up2Exercises
EXAMPLE
Write the inverse of the conditional statement.
“If you are a guitar player, then you are a musician.”
Decide whether the inverse is true or false.
Warm-Up
Exercises
Notes
• We also can write the contrapositive.
• We write the contrapositive by switching the hypothesis and
conclusion (or writing the converse) and then negating both.
• For example:
Conditional: If I play football, then I am an athlete.
Contrapositive: If I am not an athlete, then I do not play football.
Warm-Up2Exercises
EXAMPLE
Write the contrapositive of the conditional statement.
“If you are a guitar player, then you are a musician.”
Decide whether the contrapositive is true or false.
Warm-Up
Exercises
GUIDED
PRACTICE
for Example 2
Write the converse, the inverse, and the contrapositive of
the conditional statement. Tell whether each statement is
true or false.
If a dog is a Great Dane, then it is large
Warm-Up
Exercises
GUIDED
PRACTICE
for Example 2
If a polygon is equilateral, then the polygon is
regular.
Warm-Up
Exercises
Notes
When if-then statements are true both ways (the conditional
and the converse are true) then we can write them as a
biconditional statement.
In addition, any valid definition can be written as one.
Warm-Up4Exercises
EXAMPLE
Write a biconditional
Definition: If two lines intersect to form a right angle,
then they are perpendicular.
Definition: If two lines intersect to form a right angle,
then they are perpendicular.
Converse: If two lines are perpendicular, then they
intersect to form a right angle.
Biconditional: Two lines are perpendicular if and only
if they intersect to form a right angle.
Warm-Up
Exercises
GUIDED
PRACTICE
for Example 4
Rewrite the definition of acute angle as a
biconditional statement.
Warm-Up
Exercises
GUIDED
PRACTICE
for Example 4
Rewrite the statements as a biconditional.
If Mary is in theater class, she will be in the fall
play. If Mary is in the fall play, she must be taking
theater class.
Daily
Homework
Warm-Up
Exercises
Quick
CheckQuiz
For the given conditional, write the converse, the
inverse and the contrapositive. Then determine the
truth value of each.
If you are not 16, then you cannot get your driver’s
license.
Warm-Up
Exercises
For Tomorrow
Homework
HW: 2.2 (pg.75-76) #7-10,19-21,26,27