Question

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.”

Short answer

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

Step-by-step solution

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 $\mathit{e}\mathbf{\to }\mathbf{(}\mathit{a}\mathbf{\wedge }\mathbf{(}\mathit{b}\mathbf{\vee }\mathit{p}\mathbf{)}\mathbf{\wedge }\mathit{r}\mathbf{)}\mathbf{.}$