2-2
Conditional Statements
PART 2
Vocabulary
Review
1. The conditional at the right is false. Complete the counterexample below.
A whale lives in the ocean, but it is not a(n)
.
If an animal lives
in the ocean, then
it is a fish.
Vocabulary Builder
converse (noun)
KAHN
vurs
Related Words: convert, conversion
Word Source: The prefix con-, which means “together,” and vertere, which means
“to turn,” come from Latin. So, a converse involves changing the order of more than
one thing.
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Math Usage: The converse of a conditional exchanges the hypothesis and the
conclusion.
Use Your Vocabulary
Finish writing the converse of each statement.
2. Statement: If I study, then I pass the Geometry test.
Converse: If 9, then I study.
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3. Statement: If I am happy, then I laugh.
Converse: If 9, then 9.
4. Statement: If I have a summer job, then I can buy a new bicycle.
Converse: 9.
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Lesson 2-2, Part 2
Key Concept Related Conditional Statements
Statement
How to Write It
Symbols
How to Read It
Conditional
Use the given hypothesis and conclusion.
pSq
If p, then q.
Converse
Exchange the hypothesis and the conclusion.
qSp
If q, then p.
Inverse
Negate both the hypothesis and the conclusion
of the conditional.
,p S ,q
If not p, then not q.
Negate both the hypothesis and the conclusion
of the converse.
,q S ,p
If not q, then not p.
Contrapositive
Use the statement below to write each conditional.
/A measures 98, so /A is obtuse.
5. Conditional If9, then 9.
If /A measures 98, then
.
6. Converse If 9, then 9.
If
, then
.
7. Inverse If not 9, then not 9.
If
,
then
.
If
,
then
.
Problem 4 Writing and Finding Truth Values of Statements
Got It? What are the converse, inverse, and contrapositive of the conditional
statement below? 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.
Finish writing each statement.
9. Converse: If a vegetable contains beta carotene, then 9.
10. Inverse: If a vegetable is not a carrot, then 9.
11. Contrapositive: If a vegetable does not contain
beta carotene, then 9.
Chapter 2
84
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8. Contrapositive If not 9, then not 9.
12. Underline the correct word to complete each sentence.
The converse is true / false . The inverse is true / false . The contrapositive is true / false .
13. Give counterexamples for the statements that are false.
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Lesson Check • Do you UNDERSTAND?
Reasoning Suppose a conditional statement and its converse are both true.
What are the truth values of the contrapositive and inverse? How do you know?
Write T for true or F for false.
14. A conditional and its contrapositive are equivalent statements.
15. The converse and inverse of a statement are equivalent statements.
16. Equivalent statements have different truth values.
17. When a conditional statement is true, the contrapositive is true.
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18. When the converse of a statement true, the inverse is false.
19. What are the truth values of the contrapositive and inverse when a conditional
statement and its converse are both true? How do you know?
_______________________________________________________________________
_______________________________________________________________________
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Math Success
Check off the vocabulary words that you understand.
conditional
hypothesis
converse
conclusion
inverse
contrapositive
Rate how well you can write conditional statements.
Need to
review
0
2
4
6
8
Now I
get it!
10
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Lesson 2-2, Part 2