In a city, there are three types of businesses: restaurants, shops, and parks. Each business has a unique name and a unique category. There are 20 restaurants in the city, each of which has a unique name and is categorized as a restaurant. There are 15 shops in the city, each of which has a unique name and is categorized as a shop. There are 10 parks in the city, each of which has a unique name and is categorized as a park. A relation R is defined as a set of ordered pairs (business name, category) such that: (a,b)R if and only if business a is categorized as b. - Write the relation R in set-builder notation. - How many ordered pairs are in the relation R? - Is the relation R a function? Explain why or why not. - Find the inverse relation R1 - Is the relation R one-to-one? Explain why or why not. - Is the relation R onto? Explain why or why not