2) Here are two 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)} Write each relation as a set of ordered pairs. a) SoR b) RoS c) SoS

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) = dRoS(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 aSoS(b) = S(S(b)) = S(∅) = ∅,SoS(c) = S(S(c)) = S(d) = ∅ and SoS(c) = S(S(c)) = S(a) = b and cSoS(d) = S(S(d)) = S(∅) = ∅,SoS = { (a, d), (a, a), (c, b), (c, c) }