If R⊆A×B and A⊆B×C be two relations, then (S o R)-1  is equal to

S o R is relation from A to C∴ (S o R)-1is a relation from C to A.R-1is a relation from B to AS-1 is a relation from C to B.∴                R-1oS-1 is a relation from C to A.Let                (c, a)∈ SoR∴                      ∃ b ∈ B :(a, b)∈R and ( b, c) ∈S∴                             (b, a) R -1  and         (c, b) ∈ S-1∴                           ( c, a) ∈ R-1oS-1∴                            (S o R)-1⊆R-1oS-1Conversely, let (c, a) ∈ R-1 oS-1∴  ∃ b  B: (c, b)∈ S -1 and (b, a)∈R-1∴       (b, c) ∈S and (a, b)∈R⇒      (b, c) ∈S o R⇒ (c, a)∈SoR-1∴       R-1oS-1⊆(S o R)-1combining , we get        (S o R)-1= R-1oS-1