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Concept explainers
To find: the converse, inverse, and contrapositive of the given statement.
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Answer to Problem 16CYU
Theconverse and inverse of the statement is false and contrapositive is true.
Explanation of Solution
Given information:
The statement is given “if a number is divisible by 2, then it is divisible by 4”.
Consider the given statement in such manner.
Let a number is divisible by 4 can be denoted by
Converse of the statement is “if a number is divisible by 2, then it is divisible by 4”
Which is false.
Counterexample:
Find the inverse of the statement.
The inverse of the statement is “if a number is not divisible by 4, then it is not divisible by 2”
Which is the false.
Counterexample:
Find the contrapositive of the statement.
The contrapositive of the statement is “if a number is not divisible by 2, then it is not divisible by 4”
Which is true because the factors of
Therefore, theconverse and inverse of the statement is false and contrapositive is true.
Chapter 2 Solutions
Geometry, Student Edition
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