Given `A={-2,-1,0,1,2}`, list the ordered pairs determined by each of the following relations applied on A:
`R_(3)` = ''is the additive inverse of''

Answer

To find the ordered pairs determined by the relation \( R_3 \) defined as "is the additive inverse of" for the set \( A = \{-2, -1, 0, 1, 2\} \), we will follow these steps:

### Step 1: Understand the concept of additive inverse
The additive inverse of a number \( x \) is the number that, when added to \( x \), results in zero. Mathematically, if \( x \) is a number, its additive inverse is \( -x \).

### Step 2: Identify the elements of set A
The elements in set \( A \) are:
- \( -2 \)
- \( -1 \)
- \( 0 \)
- \( 1 \)
- \( 2 \)

### Step 3: Find the additive inverses for each element in A
Now, we will find the additive inverse for each element in set \( A \):

1. For \( -2 \):
- Additive inverse: \( 2 \) (since \( -2 + 2 = 0 \))
- Ordered pair: \( (-2, 2) \)

2. For \( -1 \):
- Additive inverse: \( 1 \) (since \( -1 + 1 = 0 \))
- Ordered pair: \( (-1, 1) \)

3. For \( 0 \):
- Additive inverse: \( 0 \) (since \( 0 + 0 = 0 \))
- Ordered pair: \( (0, 0) \)

4. For \( 1 \):
- Additive inverse: \( -1 \) (since \( 1 + (-1) = 0 \))
- Ordered pair: \( (1, -1) \)

5. For \( 2 \):
- Additive inverse: \( -2 \) (since \( 2 + (-2) = 0 \))
- Ordered pair: \( (2, -2) \)

### Step 4: Compile the ordered pairs
Now, we can compile all the ordered pairs we found into a set:
\[ R_3 = \{ (-2, 2), (-1, 1), (0, 0), (1, -1), (2, -2) \} \]

### Final Answer
The ordered pairs determined by the relation \( R_3 \) are:
\[ R_3 = \{ (-2, 2), (-1, 1), (0, 0), (1, -1), (2, -2) \} \]