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 find:
The converse, the inverse, and the contrapositive of each statement.
Given:
The given statement is,
If Juan wins the state lottery, then he will be rich.
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,
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
Mathematical Applications for the Management, Life, and Social Sciences
Statistics for The Behavioral Sciences (MindTap Course List)
Single Variable Calculus
Intermediate Algebra
Calculus (MindTap Course List)
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
Probability and Statistics for Engineering and the Sciences
Calculus (MindTap Course List)
Elementary Technical Mathematics
Multivariable Calculus
Calculus: Early Transcendental Functions
Calculus: An Applied Approach (MindTap Course List)
Essentials Of Statistics
Precalculus: Mathematics for Calculus (Standalone Book)
Finite Mathematics
Mathematical Excursions (MindTap Course List)
Finite Mathematics and Applied Calculus (MindTap Course List)
Single Variable Calculus: Early Transcendentals, Volume I
Essentials of Statistics for The Behavioral Sciences (MindTap Course List)
Calculus: Early Transcendentals
Understanding Basic Statistics
Elements Of Modern Algebra
Single Variable Calculus: Early Transcendentals
Trigonometry (MindTap Course List)
Contemporary Mathematics for Business & Consumers
Calculus of a Single Variable
Finite Mathematics for the Managerial, Life, and Social Sciences
Calculus: Early Transcendental Functions (MindTap Course List)
Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
Study Guide for Stewart's Multivariable Calculus, 8th