   Chapter 2.2, Problem 2E ### 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.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) 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,

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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