Concept:

If A, B and C are three sets such that  \(R\subseteq A\times B\) and \(S\subseteq B\times C\) then (SOR)-1 = R-1 O S-1. It is clear that if a R b, b S c ⇒ a S O R c.

If R is a relation from set A to set B, then inverse relation of R to be denoted by R-1, is a relation from set B to set A.

Symbolically R-1 = {(b, a): (a, b) ∈ R for all a ∈ A and b ∈ B}.

A relation R on a set A is said to be identity relation on A if R = {(a, b): a ∈ A, b ∈ A and a = b}.

A relation R from A to B is said to be the universal relation, if \(R = A\times B\).

A relation R from A to B is called an empty relation or a void relation from A to B if R = ø.

Calculation:
Given that,  A = {2, 3, 4} and B = {5, 6, 7} 

Relation R = {(a, b): a ∈ A, b ∈ B and b = a + 3}

Roster form R = {(2, 5), (3, 6), (4, 7)}

R^-1 =  {(5, 2), (6, 3), (7, 4)}

we see that,

2 → 5 → 2 ⇒ (2, 2) ∈ R^-1OR

3 → 6 → 3 ⇒ (3, 3) ∈ R-1OR

4 → 7 → 4 ⇒ (4, 4) ∈ R-1OR

Hence R-1OR = {(2, 2), (3, 3), (4, 4)}

we see that R-1OR is identity relation.