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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.

If x > 2 , then x 0 .

To determine

To find:

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

Explanation

Given:

The given statement is,

If x>2, then x0.

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,

If x>2, then x0.

The given statement is in “if P, then Q” form.

Here P is x>2 and Q is x0.

Converse of conditional statement is,

If x0, then x>2.

This statement is false because 20and2<2.

Inverse of conditional is,

If x<2, then x=0.

This statement is false because 2<2and20

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