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Found in: Page 22

Discrete Mathematics and its Applications

Book edition 7th
Author(s) Kenneth H. Rosen
Pages 808 pages
ISBN 9780073383095

You can see the movie only if you are over 18 years old or you have the permission of a parent. Express your answer in terms of m: “You can see the movie,” e: “You are over 18 years old,” and p: “You have the permission of a parent.”

The Logical proposition of the given statement is determined as ${\mathbf{m}}{\mathbf{\to }}{\mathbf{\left(}}{\mathbf{e}}{\mathbf{\vee }}{\mathbf{p}}{\mathbf{\right)}}$.

See the step by step solution

Introduction to the Concept

The statement is made up of conditionals and conjunctions.

${\mathbf{\vee }}{\mathbf{\to }}{\mathbf{OR}}{\mathbf{\wedge }}{\mathbf{\to }}{\mathbf{AND}}{\mathbf{\to }}{\mathbf{Only}}{\mathbf{}}{\mathbf{IF}}$

Solution Explanation

Now, from the given statement,

m: You can see the movie.

e: you are over 18 years old

p: you have the permission of a parent

“You are over 18 years old or you have the permission of a parent," the statement reads.

As a result, in propositional logic, ${\mathbf{e}}{\mathbf{\vee }}{\mathbf{p}}$

P if and only if Q is${\mathbf{P}}{\mathbf{\to }}{\mathbf{Q}}$

P denotes m, while Q denotes ${\mathbf{e}}{\mathbf{\vee }}{\mathbf{p}}$.

As a result, the logical proposition statement is ${\mathbf{m}}{\mathbf{\to }}{\mathbf{\left(}}{\mathbf{e}}{\mathbf{\vee }}{\mathbf{p}}{\mathbf{\right)}}$.