Answer with Step-by-step explanation:
We are given that a set {a,b,c,d}
S={(a,b),(a,c),(c,d),(c,a)}
R={(b,c),(c,b),(a,d),(d,b)]
Composition of relation:Let R and S are two relations on the given set
If ordered pair (a,b) belongs to relation R and (b,c) belongs to S .
Then, SoR={(a,c)}
By using this rule
SoR={(b,d),(b,a)}[/tex]
Because [tex](b,c)\in R[/tex] and [tex](c,d)\in S[/tex].Thus, [tex](b,d)\in SoR[/tex]
[tex](b,c))\in R[/tex] and [tex](c,a)\in S[/tex].Thus, [tex](b,a)\in SoR[/tex]
b.RoS={(a,c),(a,b),(c,b),(c,d)}
Because
[tex](a,b)\in S,(b,c)\in R[/tex] .Therefore, the ordered pair [tex](a,c)\in[/tex] RoS
[tex](a,c)\in S,(c,b)\in R[/tex] .Thus, [tex](a,b)\in RoS[/tex]
[tex](c,d)\in S,(d,b)\in R[/tex].Thus, [tex](c,b)\in RoS[/tex]
[tex](c,a)\in S,(a,d)\in R[/tex].Thus,[tex](c,d)\in RoS[/tex]
c.SoS={(a,d),(a,a),(c,c),(c,b)}
Because
[tex](a,c)\;and\; (c,d)\in S[/tex].Thus, [tex](a,d)\in SoS[/tex]
[tex](c,a),(a,b)\in S[/tex].Thus,[tex](c,b)\in SoS[/tex]
[tex](a,c)\in S[/tex] and [tex](c,a)\in S[/tex].Thus,[tex](a,a)\in SoS[/tex]
[tex](c,a)\in S[/tex] and [tex](a,c)\in S[/tex].Thus ,[tex](c,c)\in SoS[/tex]
