Question

If R be relation ‘<' from A = {1, 2, 3, 4} to B = {1, 3, 5} ie, (a, b) $ϵ$ R iff a < b, then $Ro{R}^{-1}$ is

• A. {(1, 3),(1, 5), (2, 3), (2, 5),(3, 5), (4, 5)}
• B. {(3, 1),(5, 1), (3, 2), (5, 2),(5, 3), (5, 4)}
• C. {(3, 3), (3, 5), (5, 3), (5, 5)}
• D. {(3, 3), (3, 4), (4, 5)}

Answer 1

The correct option is C {(3, 3), (3, 5), (5, 3), (5, 5)}

We have, A = {1, 2, 3, 4}, B = {1, 3, 5}
R = {(a, b) : a < b, a $ϵ$ A, b $ϵ$ B}
= {(1, 3), (1, 5), (2, 3), (2, 5), (3, 5), (4, 5)}
$\therefore R^{-1}$ = {(3,1), (5,1), (3,2), (5,2), (5,3), (5,4)}
$\therefore Ro{R}^{-1}$ = {(3,3), (3,5), (5,3), (5,5)}
The correct answer is (c).