Question

Determine if each function is one-to-one.

(a) To each person on the earth assign the number which corresponds to his age.
(b) To each country in the world, assign the latitude and longitude of its capital.
(c) To each book written by only one author, assign the author.
(d) To each country in the world which has a prime minister, assign its prime minister.

Answer 1

The functions (b), (c), and (d) are one-to-one, whereas function (a) is not one-to-one because multiple people can have the same age.

Step-by-step explanation:

The question asks whether each given function is one-to-one. A one-to-one function means that for every input, there is a unique output, and no two inputs share the same output.

• (a) To each person on the earth assign the number which corresponds to his age. This function is not one-to-one because many people can share the same age.
• (b) To each country in the world, assign the latitude and longitude of its capital. This function is one-to-one assuming that no two capital cities share the exact same latitude and longitude coordinates, which is typically the case.
• (c) To each book written by only one author, assign the author. This function is one-to-one as each book has a single unique author.
• (d) To each country in the world which has a prime minister, assign its prime minister. This function is one-to-one since each country has one prime minister, and one prime minister does not lead multiple countries.

Understanding latitude and longitude is crucial for accurately determining locations on Earth, as they serve as a global address system for mapping.