Answer
[In Exercises 1-6, translate the given statement into propositional logic using the propositions provided.]
5. 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."
Answer: e = a $\land$ r $\land$ (b $\vee$ p))
Work Step by Step
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."
We can simplify the idea of the requirements to be president into three:
You are at least 35 years old,
You have been a resident for 14 years in the country,
You are a "natural born "citizen
A natural born citizen is a person who was either born in the U.S.A, OR was born to parents who were citizens.(Hence why the question provided these two propositions)
So we can express that third requirement as b $\vee$ p,
the other two requirements are already expressed as propositions we were given, so the final expression
that determines the eligibility is just the AND of all these requirements
a $\land$ r $\land$ (b $\vee$ p))
and we know that e "You are eligible to be President of the U.S.A.," is what these requirements are for. So
e = a $\land$ r $\land$ (b $\vee$ p))
