Definition 2. 15: Let r be a relation on A, and neN. The relation rn is defined as follows (1)RO=(a, a)laEA)), we write IA (2R叶+=RRn, Theorem 2. 4: Let r be a relation on A. and m,n∈N.Then (RmoR=Rmtn (2)(Rm=Rmm
Definition 2.15: Let R be a relation on A, and nN. The relation Rn is defined as follows. (1)R0 ={(a,a)|aA}), we write IA . (2)Rn+1=RRn . Theorem 2.4: Let R be a relation on A, and m,nN. Then (1)RmRn=Rm+n (2)(Rm) n=Rmn
A={a1,a2,…,anB,B={b1,b2…,bm R,and r, be relations from a to B. RIX i, mR2=(i M RIUR2(X MRnR2=(xr∧y) V01∧01 001000 111101 Example:A={2,3,4},B={1,3,5,7 R1={(2,3),(2,5),2,7),(3,5)、3,7),(45),(4,7) R2={(25)3,3),(4,1)4,7) Inverse relation R-I of R: MpMp, Mp is the transpose of M R
A={a1 ,a2 ,,an },B={b1 ,b2 ,,bm} R1 and R2 be relations from A to B. MR1=(xij), MR2=(yij) MR1∪R2=(xijyij) MR1∩R2=(xijyij) 0 1 0 1 0 0 1 0 0 0 1 1 1 1 0 1 Example:A={2,3,4},B={1,3,5,7} R1={(2,3),(2,5),(2,7),(3,5),(3,7),(4,5),(4,7)} R2={(2,5),(3,3),(4,1),(4,7)} Inverse relation R-1 of R : MR-1=MR T , MR T is the transpose of MR