   Chapter 2.2, Problem 1E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

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 Juan wins the state lottery, then he will be rich.

To determine

To find:

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

Explanation

Given:

The given statement is,

If Juan wins the state lottery, then he will be rich.

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 Juan wins the state lottery, then he will be rich.

The conditional statement of the given statement is,

If Juan is the winner of the lottery, then he is rich.

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

Here P is Juan is the winner of the lottery and Q is he is rich.

Converse of conditional statement is,

If Juan is rich, then he is the winner of the lottery.

This statement is false because Juan may have been rich without being winner of the lottery.

Inverse of conditional is,

If Juan is not the winner of the lottery, then he will not be rich

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