(1) Explain the words relation and function. Include in your explanation how the meanings of the two words differ. Give a real-world example of a relation that is not a function. Is it possible to give an example of a function that is not a relation? If so, give one. If not, explain why it is not possible.
I ezinieznsnlskdkdo
(1) The words "relation" and "function" both refer to mathematical concepts, but they have distinct meanings.
A relation is a general term that describes the association between two sets of elements. It can be thought of as a set of ordered pairs, where each pair consists of an element from the first set and an element from the second set. The elements can be numbers, objects, or any other type of entity. Relations can have different properties, such as being reflexive, symmetric, or transitive.
On the other hand, a function specifically describes a relation where each element from the first set has exactly one corresponding element in the second set. Put simply, a function assigns one output value to each input value, and no input value maps to more than one output value. This property is known as the vertical line test, which states that a vertical line drawn through the graph of a function will intersect the graph at most once.
For example, consider a relation between the set of people and their heights. Each person is associated with a certain height, forming a relation. In this case, if two people have the same height, the relation is still valid.
Now, let's discuss a relation that is not a function. One example is a relation between the set of students and their grades on a test. In this case, if a student has multiple grades for the same test, the relation fails to meet the definition of a function since a student (input) is associated with more than one grade (output). Hence, it violates the one-to-one mapping requirement of a function.
In mathematics, a function is a specific type of relation. By definition, every function is a relation. Therefore, it is not possible to give an example of a function that is not a relation because a function inherently falls under the broader concept of a relation.