Question

Adding which of the following ordered pairs to the set {(0, 1), (2, 4), (3, 5)} would make it not a function?

(1, 6)
(4, 2)
(0, 7)
(7, 0)

Answer 1

A set of ordered pairs represents a function if every first element (input) is associated with exactly one second element (output). To determine which ordered pair to add would make the set not a function, we need to check if adding that pair would create a situation where a first element corresponds to more than one second element.

The current set is \(\{(0, 1), (2, 4), (3, 5)\}\). Here, each first element (0, 2, 3) is unique.

Now, let's explore adding each of the given pairs:

1. **(1, 6)**:
- This adds a new first element (1) which does not exist in the current set. It would not make the set not a function.

2. **(4, 2)**:
- This also introduces a new first element (4). The set remains a function.

3. **(0, 7)**:
- This pair has the first element (0), which is already present in the set. The existing output associated with (0) is 1. Adding (0, 7) would mean that 0 maps to both 1 and 7, which violates the definition of a function. Therefore, this would make the set not a function.

4. **(7, 0)**:
- This pair introduces yet another new first element (7). It does not affect any existing mappings and would keep the set as a function.

Given this analysis, the ordered pair that, when added to the set, would make it not a function is:

**(0, 7)**.