The correct option is C R−1oS−1
SoR is relation from A to C.
∴ (SoR)−1 is a relation from C to A.
R−1 is a relation from B to A.
S−1 is a relation from C to B.
∴ R−1 0S−1 is a relation from C to A.
Let (C,a) ϵ (SoR)−1. ∴ (a,c) ϵ SoR
∴ ∃ b ϵ B : (a,b) ϵ R and (b,c) ϵ s
∴ (b,a) ϵ R−1 and (c,b) ϵ S−1
∴ (c, a) ϵ R−1 oS−1
∴(SoR)−1 ⊑ R−1 oS−1
Conversely, Let (c, a) ϵ R−1 oS−1
∴ ∃ b ϵ B : (c, b) ϵ S−1 and (b,a) ϵ R−1
∴ (b,c) ϵ S and (a,b) ϵ R
Rightarrow (a,c) ϵ S and (a,b) ϵ R
⇒ (a,c) ϵ SoR ⇒ (c,a) ϵ (SoR)−1
∴ R−1oS−1⊑(SoR)−1
Combining, we get (SoR)−1=R−1oS−1