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Elementary Geometry for College St...
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Elementary Geometry for College St...
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 find:
The converse, the inverse, and the contrapositive of each statement.
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) | If P, then Q. | |
| Converse of conditional | If Q, then P. | |
| Inverse of conditional | If not P, then not Q. | |
| Contrapositive of conditional | 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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