Answer:
Given relations defined on the set {a, b, c, d},
S= { (a, b), (a, c), (c, d), (c, a)}
R={ (b, c), (c, b), (a, d), (d, b)},
Since, SoR(x) = S(R(x)),
So, SoR(a) = S(R(a)) = S(d) = ∅,
SoR(b) = S(R(b)) = S(c) = d and a,
SoR(c) = S(R(c)) = S(b) = ∅,
SoR(d) = S(R(d)) = S(b) = ∅,
Thus, SoR = { (b,d), (b,a) }
RoS(a) = R(S(a)) = R(b) = c and RoS(a) = R(S(a)) = R(c) = b,
RoS(b) = R(S(b)) = R(∅) = ∅,
RoS(c) = R(S(c)) = R(d) = b and RoS(c) = R(S(c)) = R(a) = d
RoS(d) = R(S(d)) = R(∅) = ∅,
Thus, RoS = { (a, c), (a, b), (c,d), (c, b) },
SoS(a) = S(S(a)) = S(b) = ∅ and SoS(a) = S(S(a)) = S(c) = d and a
SoS(b) = S(S(b)) = S(∅) = ∅,
SoS(c) = S(S(c)) = S(d) = ∅ and SoS(c) = S(S(c)) = S(a) = b and c
SoS(d) = S(S(d)) = S(∅) = ∅,
SoS = { (a, d), (a, a), (c, b), (c, c) }
