Question

the relation R : A  B, where A = { 1,2,3} and B = {1,3,5} is defined by
R = { (x,y):x<y,x∈A,y∈B}, then​

Answer 1

Step-by-step explanation:

As given in the question

R={

(1,3)

(2,5)

(1,5)

(3,5)

(2,3)

(4,5)

}

Therefore, R

−1

={

(3,1)

(5,2)

(5,1)

(5,3)

(3,2)

(5,4)

}

Now if R and S are two relations then ROS has elements (x,z) if (x,y)∈S and (y,z)∈R.

Thus, for two relations R and R

−1

, applying above result we get ROR

−1

={

(3,3),(3,5),(5,3),(5,5)

}

Answer 2

Answer:

Given the relation R:A→B where A={1,2,3,4},B={1,3,5} is defined by R={(x,y):x<y,x∈A,y∈B}.

R={(2,1),(3,1),(4,1),(4,3)}.

And R

−1

={(1,2),(1,3),(1,4),(3,4)}.