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Elementary Geometry for College St...

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

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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) PQ If P, then Q.
Converse of conditional QP If Q, then P.
Inverse of conditional PQ If not P, then not Q.
Contrapositive of conditional QP 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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