Concept explainers
To find: the converse, inverse, and contrapositive of the given statement.
Answer to Problem 47PPS
The converse and inverse of the statement is false and contrapositive is true.
Explanation of Solution
Given information:
The statement is given “if you live in Chicago, you live in Illinois”.
Find the converse of the given statement.
Converse of the statement is “if you live in Illinois, you live in Chicago”
Which is false.
Counterexample:
You could live in Springfield.
Find the inverse of the statement.
The inverse of the statement is “if you do not live in Chicago, you do not live in Illinois”
Which is the false.
Counterexample:
You could live in Springfield.
Find the contrapositive of the statement.
The contrapositive of the statement is “if you do not live in Illinois, you do not live in Chicago”
Which is true.
Therefore, the converse and inverse of the statement is false and contrapositive is true.
Chapter 2 Solutions
Geometry, Student Edition
Additional Math Textbook Solutions
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