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 0 R-1 is (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)  (3.5)

Tardigrade Admin · Accepted Answer

Since R = beginBmatrix(1.3)&(1.5)&(2.3) (2.5)&(3.5)&(4.5) endBmatrix and R-1 = beginBmatrix(3.1)&(5.1)&(3.2) (5.2)&(5.3)&(5.4) endBmatrix Thus, R0R-1 = beginBmatrix(3.5)&(5.5) (3.3)&(5.3) endBmatrix

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 $R 0 R^{- 1}$ is

${(1.3), (1.5), (2.3), (2.5), (3.5), (4.5)}$

${(3.1), (5.1), (5.2), (5.3), (5.4)}$

${(3.3), (3.5), (5.3), (5.5)}$

${(3.5)}$

Since $R = {(1.3) (2.5) (1.5) (3.5) (2.3) (4.5)}$ and
$R^{- 1} = {(3.1) (5.2) (5.1) (5.3) (3.2) (5.4)}$
Thus, $R 0 R^{- 1} = {(3.5) (3.3) (5.5) (5.3)}$

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 R0R−1 is

{(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)}

{(3.5)}