Concept explainers
To find: The converse, inverse, and contrapositive of each true conditional. If a statement is false then find a counterexample.
Answer to Problem 4BCYP
The converse, inverse, and contrapositive of given conditional statement is below.
Explanation of Solution
Given:
The given conditional statement is:
A hamster is a rodent.
First rewrite the conditional in if-then form, as below.
If an animal is a hamster, then it is a rodent.
Based on the information at the left, this statement is true.
The converse of the conditional statement is as below.
If an animal is a rodent, then it is a hamster.
Counterexample: A squirrel is a rodent, but it is not a hamster.
Therefore, the converse is false.
The inverse of the conditional statement is given as:
If an animal is not a hamster, then it is not a rodent.
Counterexample: A squirrel is not a hamster, but it is a rodent.
Therefore, the inverse is false.
The contrapositive of the conditional statement is given below.
If an animal is not a rodent, then it is not a hamster.
Based on the information at the left, this statement is true.
Check to see that logically equivalent statements have the same truth value.
Both the conditional and contrapositive are true.
Both the converse and inverse are false.
Therefore the logically equivalent statements have the same truth value.
Chapter 2 Solutions
Geometry, Student Edition
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