Question

For the following statement, determine whether an inclusive “OR” or exclusive “OR” is used. Give reasons for your answer.
To enter a country, you need a passport or a voter registration card.

Answer 1

Hint: It is given that our statement is “To enter a country, you need a passport or a voter registration card.” It means that a person having either a passport or a voter registration card can also enter a country. We know that an inclusive “OR” is a logical connective that joins two or more predicates and yields the logical value "true" when at least one of the predicates is true. Now, solve it further and conclude the statement, whether it is inclusive or exclusive.

Complete step-by-step solution:
According to the question, we have a statement given and we have to determine whether an inclusive “OR” or exclusive “OR” is used. The given statement is,
To enter a country, you need a passport or a voter registration card ……………………………..(1)
Now, understanding the meaning of the given statement. The statement says that for a person willing to enter a country, he needs a passport or a voter registration card. We can see that “or” is used in the given statement.
It means that a person having only a passport can also enter a country …………………………...(2)
From equation (1), we have the given statement.
In other words, we can also say that a person can also enter a country if he has a voter registration card only …………………………..(3)
A person having both passport and voter registration cards can also enter a country …………………………………..(4)
Now, from equation (2), equation (3), and equation (4), we can say that
A person can enter a country if he has either passport, or voter registration card, or both …………………………………..(5)
We know that an inclusive “OR” is a logical connective that joins two or more predicates and yields the logical value "true" when at least one of the predicates is true …………………….……..(6)
Now, from equation (5) and equation (6), we can conclude that the “OR” used in the given statement is an inclusive “OR”.
Hence, an inclusive “OR” is used in the given statement.

Note: In this question, one might make a silly mistake and think that to enter a country a person needs both a passport and a voter registration card. This is wrong because it is given that a person needs a passport or a voter registration card. So, we can say that a person can enter a country if he has either a passport, or voter registration card, or both.