The range of a relation is defined as the set of all second elements of the ordered pairs in that relation. In your case, the relation consists of the following pairs: (3, 2), (1, 2), (1, 4), and (1, 2).
To find the range, we need to extract the second elements from each ordered pair:
- From (3, 2), we have 2.
- From (1, 2), we again have 2.
- From (1, 4), we have 4.
- From the second (1, 2), we have 2 once more.
Next, we compile these second elements: 2, 2, 4, and 2. However, since we are interested in the unique values for the range, we eliminate the duplicates.
Thus, the unique values are:
- 2
- 4
Consequently, the range of the relation is:
- {2, 4}
This provides a clear understanding that the relation’s range consists of the values that are output from the first elements of the ordered pairs, emphasizing the importance of unique entries in determining the range.