If RAB and SBC 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 A
S-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)-1R-1oS-1
Conversely, 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
(a, c) S o R (c, a)(S o R)-1
R-1oS-1(S o R)-1
combining , we get
(S o R)-1= R-1oS-1