   Chapter 2.2, Problem 4E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# Note: Exercises preceded by an asterisk are of a more challenging nature.In Exercises 1 to 4, write the converse, the inverse, and the contrapositive of each statement. When possible, classify the statement as true or false.In a plane, if two lines are not perpendicular to the same line, then these lines are not parallel.

To determine

To find:

The converse, the inverse, and the contrapositive of each statement.

Explanation

Given:

The given statement is,

In a plane, if two lines are not perpendicular to the same line, then these lines are not parallel.

Approach:

 Conditional (or Implication) P→Q If P, then Q. Converse of conditional Q→P If Q, then P. Inverse of conditional ∼P→∼Q If not P, then not Q. Contrapositive of conditional ∼Q→∼P If not Q, then not P.

Consider the given statement,

In a plane, if two lines are not perpendicular to the same line, then these lines are not parallel.

The converse, the inverse, and the contrapositive of given statement are given by table (1).

 Converse of conditional In a plane, if two lines are not parallel, then these lines are not perpendicular to the same line

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