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).

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Accepted Answer

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.

Answer

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.

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 \(R\).

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