To determine which scenario exhibits a functional relation, we first need to understand what a function is in mathematical terms. A function is a relation where each element in the domain (the first set) is related to exactly one element in the codomain (the second set). Let's go through each option to see which satisfies this condition:
1. The set of tree heights and the set of trees in a forest:
- In this scenario, the domain is the set of tree heights, and the codomain is the set of trees in a forest.
- Multiple trees can have the same height.
- Therefore, one height can be associated with multiple trees, which means this does not exhibit a functional relation.
2. The set of car make and models and the set of people in a certain town:
- Here, the domain is the set of car make and models, and the codomain is the set of people in a certain town.
- Multiple people can own the same car make and model.
- Therefore, one car model can be associated with multiple people, so this also does not exhibit a functional relation.
3. The set of birthdays and the set of students in a class:
- The domain in this case is the set of birthdays, and the codomain is the set of students in a class.
- Multiple students can share the same birthday.
- Therefore, one date (birthday) can be associated with multiple students, thus this does not exhibit a functional relation.
4. The set of people with Social Security cards and the set of Social Security numbers:
- In this scenario, the domain is the set of people with Social Security cards, and the codomain is the set of Social Security numbers.
- Each Social Security number is unique and is issued to exactly one person.
- Therefore, each Social Security number is associated with exactly one individual, which satisfies the condition of a functional relation.
Given the analysis, the scenario that exhibits a functional relation is:
The set of people with Social Security cards and the set of Social Security numbers.
So, the correct answer is: 4.
