Given two relations \(R = \{(2, 3), (4, 5), (6, 7)\}\) and \(S = \{(3, 2), (5, 4), (7, 6)\}\), determine if relation \(S\) is the inverse of relation \(R\).

Step 1 ：Step 1: Define the inverse relation of \(R\), denoted as \(R^{-1}\). The inverse relation of \(R\) is obtained by swapping the first and second elements of each ordered pair in \(R\).

Step 2 ：Step 2: Calculate the inverse relation of \(R\), which is \(R^{-1} = \{(3, 2), (5, 4), (7, 6)\}\).

Step 3 ：Step 3: Compare \(R^{-1}\) with \(S\). If they are the same, then \(S\) is the inverse of \(R\), otherwise it is not.