The range of a relation is the set of all second elements (outputs) from the ordered pairs in that relation.
In the given relation R, we can look at each ordered pair:
- (3, 5) – Here, the second element is 5.
- (1, 2) – The second element is 2.
- (1, 4) – The second element is 4.
- (1, 2) – Again, the second element is 2, but since we already counted it, we won’t count it again.
Now, compiling the unique second elements, we have:
- 5
- 2
- 4
Thus, the range of the relation R is {2, 4, 5}.