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Q9

Expert-verifiedFound in: Page 34

Book edition
Student Edition

Author(s)
Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Pages
227 pages

ISBN
9780395977279

Provide a counterexample to show that each statement is false. You may use words or draw a diagram.

If a line lies in a vertical plane, then the line is vertical.

The counterexample is a wall of the room as a vertical plane, wherein the lines where the wall and the ceiling intercept are horizontal lines, but they still lie in the plane.

The counterexample is an example for which a hypothesis is true but the conclusion is false for an if-then statement.

In order to find a counterexample for the statement “If a line lies in a vertical plane, then the line is vertical.” we need to find a vertical plane wherein a line lies which is not specifically vertical.

If we look at the wall of the room as a vertical plane, then the lines where the wall and the ceiling intercept are horizontal lines, but they lie in the plane.

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