If {(3,2),(4,2),(3,1),(7,1),(2,3)} is to be a function, which one of the following must be removed from the set?

Options

A. (3,2)
B. (4,2)
C. (2,3)
D. (7,1)

Explanation

To determine which ordered pair must be removed from the set \(\{(3,2),(4,2),(3,1),(7,1),(2,3)\}\) for it to be a function, we need to recall the definition of a function. A function is a relation where each input (or first element of the ordered pair) corresponds to exactly one output (or second element of the ordered pair).

### Step-by-Step Solution:

1. **Identify the Ordered Pairs**:
The given set of ordered pairs is \(\{(3,2),(4,2),(3,1),(7,1),(2,3)\}\).

2. **List the Inputs**:
The inputs (first elements) from the ordered pairs are:
- From (3,2): 3
- From (4,2): 4
- From (3,1): 3
- From (7,1): 7
- From (2,3): 2

So, the list of inputs is \(\{3, 4, 3, 7, 2\}\).

3. **Check for Duplicates**:
We see that the input 3 appears twice (in the pairs (3,2) and (3,1)). This means that the input 3 corresponds to two different outputs: 2 and 1.

4. **Determine Which Pair to Remove**:
Since a function cannot have the same input mapping to multiple outputs, we need to remove one of the pairs that contain the input 3. We have two options:
- Remove (3,2)
- Remove (3,1)

5. **Select the Correct Option**:
The question asks which one must be removed from the set. If we look at the options provided (not given in the question but assumed to be related to pairs), we find that (3,2) is one of the options. Therefore, we can conclude that removing (3,2) will make the relation a function.

### Conclusion:
The ordered pair that must be removed from the set to make it a function is **(3,2)**.