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

Answer

To solve the problem, we need to find all ordered pairs \((m, n)\) such that \(m\) is the square of \(n\) for the set \(A = \{-2, -1, 0, 1, 2\}\). This means we are looking for pairs where \(m = n^2\).

### Step-by-step Solution:

1. **Identify the elements of set A**:
The set \(A\) consists of the elements \(-2, -1, 0, 1, 2\).

2. **Calculate the squares of each element in A**:
- The square of \(-2\) is \(4\) (not in A).
- The square of \(-1\) is \(1\) (in A).
- The square of \(0\) is \(0\) (in A).
- The square of \(1\) is \(1\) (in A).
- The square of \(2\) is \(4\) (not in A).

3. **List the ordered pairs**:
We need to find all pairs \((m, n)\) such that \(m = n^2\):
- For \(n = -1\), \(m = (-1)^2 = 1\) → Ordered pair: \((-1, 1)\)
- For \(n = 0\), \(m = 0^2 = 0\) → Ordered pair: \((0, 0)\)
- For \(n = 1\), \(m = 1^2 = 1\) → Ordered pair: \((1, 1)\)
- For \(n = -2\) and \(n = 2\), the squares are \(4\) which is not in \(A\), so no pairs can be formed.

4. **Final list of ordered pairs**:
The ordered pairs that satisfy the relation \(R_2\) are:
- \((-1, 1)\)
- \((0, 0)\)
- \((1, 1)\)

Thus, the relation \(R_2\) can be expressed as:
\[ R_2 = \{(-1, 1), (0, 0), (1, 1)\} \]