## Getting acquainted with metrics

### Task number: 3163

For the set \(X\) and function \(\rho\colon X^2 \to \mathbb R\) determine whether the function \(\rho\) is a metric.

#### Variant 1

\(X = \{1, 2, 3, 4, 5\}\) a \(\rho\) is given by the table:

1 2 3 4 5 1 0 2 6 4 4 2 2 0 3 2 4 3 6 3 0 2 4 4 4 2 2 0 4 5 4 4 4 4 0 #### Variant 2

\(X = \{1, 2, 3, 4, 5\}\) a \(\rho\) is given by the table:

1 2 3 4 5 1 0 5 6 5 3 2 5 0 5 8 4 3 6 5 0 5 3 4 5 8 5 0 4 5 3 4 3 4 0