To determine which relation does not represent a function, we need to recall the definition of a function. A relation is a function if every element in the domain (the set of all first coordinates) is associated with exactly one element in the range (the set of all second coordinates). In other words, no two ordered pairs can have the same first element with different second elements.
Let's analyze each relation given:
### Relation A: {(3,0), (0, 3)}
- In this relation, the first elements are 3 and 0.
- Both 3 and 0 are associated with a unique second element.
- Hence, Relation A is a function.
### Relation B: {(6,-2), (5,-2)}
- In this relation, the first elements are 6 and 5.
- Both 6 and 5 are associated with a unique second element.
- Hence, Relation B is a function.
### Relation C: {(3, 4), (3, 5)}
- In this relation, the first element 3 appears twice.
- The element 3 is associated with two different second elements: 4 and 5.
- This means that Relation C is not a function because 3 does not have a unique second element.
### Relation D: {(5, 5), (-5,-5)}
- In this relation, the first elements are 5 and -5.
- Both 5 and -5 are associated with a unique second element.
- Hence, Relation D is a function.
### Relation E: {(1,-2), (-2, 1)}
- In this relation, the first elements are 1 and -2.
- Both 1 and -2 are associated with a unique second element.
- Hence, Relation E is a function.
From this analysis, we can see that the relation that does not represent a function is:
Relation C: {(3, 4), (3, 5)}
Thus, the correct answer is:
○ C. {(3, 4), (3, 5)}
