If the relation R:A→ B, where A = 1,2,3, 4 and B = 1,3,5 is defined by R= (x,y):x

Question

If the relation R:A→ B, where A = 1,2,3, 4 and B = 1,3,5 is defined by R= (x,y):x<y,x∈ A,y∈ B ,then R-1oR is equal to (A)  1,3),(1,5),(2,3),(2,5),(3,5),(4,5)  (B)  (3,1),(5,1),(5,2),(5,3),(5,4)  (C)  (3,3),(3,5),(5,3),(5,5)  (D) None of the above

Tardigrade Admin · Accepted Answer

∵ R= (1,3),(1,5),(2,3),(2,5),(3,5),(4,5) and R-1= (3,1),(5,1),(3,2),(5,2),(5,3),(5,4) Thus, R-1oR= (3,5),(5,5),(3,3),(5,3)

Q. If the relation $R : A \to B,$ where A = {1,2,3, 4} and B = {1,3,5} is defined by $R = {(x, y) : x < y, x \in A, y \in B},$ ,then $R^{- 1} o R$ is equal to

${1, 3), (1, 5), (2, 3), (2, 5), (3, 5), (4, 5)}$

${(3, 1), (5, 1), (5, 2), (5, 3), (5, 4)}$

${(3, 3), (3, 5), (5, 3), (5, 5)}$

None of the above

$∵$ $R = {(1, 3), (1, 5), (2, 3), (2, 5), (3, 5), (4, 5)}$ and $R^{- 1} = {(3, 1), (5, 1), (3, 2), (5, 2), (5, 3), (5, 4)}$ Thus, $R^{- 1} o R = {(3, 5), (5, 5), (3, 3), (5, 3)}$

Q. If the relation R:A→B, where A = {1,2,3, 4} and B = {1,3,5} is defined by R={(x,y):x<y,x∈A,y∈B}, ,then R−1oR is equal to

{1,3),(1,5),(2,3),(2,5),(3,5),(4,5)}

{(3,1),(5,1),(5,2),(5,3),(5,4)}

{(3,3),(3,5),(5,3),(5,5)}