Question

A relation is given below.

{(0, 0), (2, 0.5), (4, 1), (3, 1.5), (4, 2), (5, 1.5), (6, 8)}

Which ordered pair can be removed to make this relation a function?


Why would removing this ordered pair make the relation a function?

Answer 1

To determine which ordered pair can be removed to make the relation a function, we need to understand the definition of a function. A relation is a function if every input (or first element of the ordered pair) has exactly one corresponding output (or second element).

Now, let's examine the ordered pairs in the given relation:

- (0, 0)
- (2, 0.5)
- (4, 1)
- (3, 1.5)
- (4, 2)
- (5, 1.5)
- (6, 8)

From this list, we see that the input "4" appears twice:

1. (4, 1)
2. (4, 2)

Since the input "4" has two different outputs (1 and 2), this violates the definition of a function.

To make this relation a function, we can remove either (4, 1) or (4, 2).

**Removing (4, 1)**:
The resulting relation would be:
{(0, 0), (2, 0.5), (4, 2), (3, 1.5), (5, 1.5), (6, 8)}

**Removing (4, 2)**:
The resulting relation would be:
{(0, 0), (2, 0.5), (4, 1), (3, 1.5), (5, 1.5), (6, 8)}

In either case, the input "4" would only be associated with one output, which satisfies the condition for being a function.

**Conclusion**:
Removing either (4, 1) or (4, 2) will make the relation a function because it ensures that each input has only one corresponding output.