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Expert-verified Found in: Page 22 ### Discrete Mathematics and its Applications

Book edition 7th
Author(s) Kenneth H. Rosen
Pages 808 pages
ISBN 9780073383095 # You are eligible to be President of the U.S.A. only if you are at least 35 years old, were born in the U.S.A, or at the time of your birth both of your parents were citizens, and you have lived at least 14 years in the country. Express your answer in terms of e: “You are eligible to be President of the U.S.A.,” a: “You are at least 35 years old,” b: “You were born in the U.S.A,” p: “At the time of your birth, both of your parents where citizens,” and r: “You have lived at least 14 years in the U.S.A.”

The logical proposition of the given statement is determined as, ${\mathbf{e}}{\mathbf{\to }}{\mathbf{\left(}}{\mathbf{a}}{\mathbf{\wedge }}{\mathbf{\left(}}{\mathbf{b}}{\mathbf{\vee }}{\mathbf{p}}{\mathbf{\right)}}{\mathbf{\wedge }}{\mathbf{r}}{\mathbf{\right)}}$ .

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## Introduction to the Concept

"If-then" is a logical sign. It can be depict as ${\mathbf{\to }}$.

"or" is a logical sign. It can be depict as ${\mathbf{\vee }}$.

"and" is a logical sign. It can be depict as role="math" localid="1668082747506" ${\mathbf{\wedge }}$.

## Solution Explanation

The given statements are,

e: You are eligible to be President of the U.S.A

a: You are at least 35 years old

b: You were born in the U.S.A

p: At the time of your birth, both of your parents where citizens

r: You have lived at least 14 years in the U.S.A

The propositional logic statement is given as follows,

You are eligible to be President of the U.S.A. only if you are at least 35 years old, were born in the U.S.A, or at the time of your birth both of your parents were citizens, and you have lived at least 14 years in the country.

In propositional logic, the statement is ${\mathbit{e}}{\mathbf{\to }}{\mathbf{\left(}}{\mathbit{a}}{\mathbf{\wedge }}{\mathbf{\left(}}{\mathbit{b}}{\mathbf{\vee }}{\mathbit{p}}{\mathbf{\right)}}{\mathbf{\wedge }}{\mathbit{r}}{\mathbf{\right)}}{\mathbf{.}}$ ### Want to see more solutions like these? 