2-2 Conditional Statements
OBJECTIVES: Recognize conditional statements and their parts; write converses, inverses, and
contrapositives of conditionals.
page 37 - SC
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 driver could be
False.
False.
TRUE
too close and he
cannot read the
bumper sticker.
The driver is not
wearing necessary
reading glasses and
he cannot read the
bumper sticker.
2-2 Conditional Statements
OBJECTIVES: Recognize conditional statements and their parts; write converses, inverses,
and contrapositives of conditionals.
You can describe some mathematical relationships using a variety of if-then statements. The study of
if-then statements and their truth values is a foundation of reasoning.
page 49- HH
page 38 - SC
Identifying the Hypothesis and the Conclusion
What are the hypothesis and the
conclusion of the conditional?
If an angle measures 130, then
the angle is obtuse.
HYPOTHESIS:
An angle measures 130.
CONCLUSION:
The angle is obtuse.
2-2 Conditional Statements
OBJECTIVES: Recognize conditional statements and their parts; write converses, inverses,
and contrapositives of conditionals.
page 51 -- SC
page 38 - SC
mammals
dolphins
If the animal is a dolphin, then it is a mammal..
2-2 Conditional Statements
OBJECTIVES: Recognize conditional statements and their parts; write converses, inverses,
and contrapositives of conditionals.
page 50- HH
2-2 Conditional Statements
OBJECTIVES: Recognize conditional statements and their parts; write converses, inverses,
and contrapositives of conditionals.
Page 38 - SC
2-2 Conditional Statements
OBJECTIVES: Recognize conditional statements and their parts; write converses, inverses,
and contrapositives of conditionals.
Page 39 - SC
False;
January has 28 days, plus 3more.
True
Identifying and Determining the Validity of Statements
What are the converse, inverse, and contrapositive of the following conditional?
What are the truth values of each? If a statement is false, give a counterexample.
If a vegetable is a carrot, then it contains beta carotene.
Converse: If a vegetable contains beta carotene, then it is a carrot.
 FALSE ; spinach…
Inverse: If a vegetable is not a carrot, then it does not contains beta carotene.
Contrapositive: If a vegetable does not contain beta carotene, then it is not a carrot.
FALSE ;
spinach…
 TRUE
2-2 Conditional Statements
OBJECTIVES: Recognize conditional statements and their parts; write converses, inverses,
and contrapositives of conditionals.
Page 40 - SC
1. What are the converse, inverse, and contrapositive of the statement?
Which statements are true?
TRUE
If a figure is a rectangle with sides 2 cm and 3 cm, then it has a perimeter of 10 cm. 
Converse: If a figure has a perimeter of 10 cm, then it is a rectangle with sides 2 cm and 3 cm.
Inverse: If a figure is not a rectangle with sides 2 cm and 3 cm,
then it does not have a perimeter of 10 cm.
Contrapositive: If a figure does not have a perimeter of 10 cm,
then it is not a rectangle with sides 2 cm and 3 cm.
 FALSE
 TRUE
2. Write a conditional statement that matches the Venn diagram shown.
Then write the converse of the statement and determine whether it is true.
CONDITIONAL: If an object is a yacket, then it is a widget.
CONVERSE: If an object is a widet, then it is a yacket.

FALSE
2-2 Conditional Statements
OBJECTIVES: Recognize conditional statements and their parts; write converses, inverses,
and contrapositives of conditionals.
Page 41 - SC
Exchange and negate the hypothesis and conclusion.
No; the hypothesis and conclusion were exchanged.
The conditional should be “If it is Sunday, then you jog.”
Both are true because a conditional and its contrapositive will always have
the same truth value, and a converse and an inverse have the same truth value.
Page 42 - SC
Page 42- SC
Inverse: If a movie is not a comedy, then it is not funny.