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

Answer

To find the ordered pairs determined by the relation \( R_1 \) defined as "is less than" on the set \( A = \{-2, -1, 0, 1, 2\} \), we will follow these steps:

### Step 1: Understand the Relation
The relation \( R_1 \) means that for any two elements \( m \) and \( n \) in set \( A \), the ordered pair \( (m, n) \) is included in the relation if \( m < n \).

### Step 2: List All Possible Ordered Pairs
We will consider each element in set \( A \) and find all elements that are greater than it to form the ordered pairs.

1. **For \( m = -2 \)**:
- Possible \( n \) values: \( -1, 0, 1, 2 \)
- Ordered pairs:
- \( (-2, -1) \)
- \( (-2, 0) \)
- \( (-2, 1) \)
- \( (-2, 2) \)

2. **For \( m = -1 \)**:
- Possible \( n \) values: \( 0, 1, 2 \)
- Ordered pairs:
- \( (-1, 0) \)
- \( (-1, 1) \)
- \( (-1, 2) \)

3. **For \( m = 0 \)**:
- Possible \( n \) values: \( 1, 2 \)
- Ordered pairs:
- \( (0, 1) \)
- \( (0, 2) \)

4. **For \( m = 1 \)**:
- Possible \( n \) value: \( 2 \)
- Ordered pair:
- \( (1, 2) \)

5. **For \( m = 2 \)**:
- There are no \( n \) values greater than \( 2 \), so no pairs can be formed.

### Step 3: Combine All Ordered Pairs
Now, we will compile all the ordered pairs we found:

- From \( m = -2 \): \( (-2, -1), (-2, 0), (-2, 1), (-2, 2) \)
- From \( m = -1 \): \( (-1, 0), (-1, 1), (-1, 2) \)
- From \( m = 0 \): \( (0, 1), (0, 2) \)
- From \( m = 1 \): \( (1, 2) \)

### Final List of Ordered Pairs
The complete set of ordered pairs for the relation \( R_1 \) is:
\[ R_1 = \{ (-2, -1), (-2, 0), (-2, 1), (-2, 2), (-1, 0), (-1, 1), (-1, 2), (0, 1), (0, 2), (1, 2) \} \]