Question

Suppose a relation R=\ (1,4),(2,5) , (4,4),(6,5)\ is defined from A to B. Find the inverse of R. Also, find the domain and range of R ^ - 1 ?​

Answer 1

Answer:

(i) To obtain the elements of R oR, we proceed as follows. Since (1, 4) ∈ R and ( 4, 5)∈ R we have (1, 5) ∈ R o R.

Again since ( 1, 4) ∈ R and ( 4, 5) ∈ R  we have (1, 6) ∈ R o R.

Similarly (3, 6) ∈ RoR since (3, 7) ∈ R and (7, 6) ∈ R 

Hence R o R = (1, 5), ( 1, 6), (3, 6)

(ii) We first find R−1.

We have R−1 = {(5,4), ( 4, 1), (6, 4), (6, 7), (7, 3)}

We now obtain the elements of R−1o R. We first pick the element of R and then R−1 

Since (4, 5) ∈ R and (5, 4) ∈R−1  We have (4, 4) ∈ R−1oR

Similarlly 

(1,4)∈R,(4,1)∈R−1⇒(1,1)∈R−1oR.

(4,6)∈R,(6,4)∈R−1⇒(4,4)∈R−1oR.

(4,6)∈R,(6,7)∈R−1⇒(4,7)∈R−1oR.

(7,6)∈R,(6,4)∈R−1⇒(7,4)∈R−1oR.

(7,6)∈R,(6,7)∈R−1⇒(7,7)∈R−1oR.

(3,7)∈R,(7,3)∈R−1⇒(3,3)∈