Question

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 1

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) }