A={a1;a2,…,an3,B={b1,b2,…,bm}, C={c1,C2,,}, Ri be a relations from a to B, MRi(Xi )mxn, R2 be a relation from b to c. m R2 (y )nyr The n r composition R2r, ofr and r22 MRoR-((Xk Ayn)
A={a1 ,a2 ,,an },B={b1 ,b2 ,,bm }, C={c1 ,c2 ,,cr }, R1 be a relations from A to B, MR1=(xij)mn , R2 be a relation from B to C, MR2=(yij) nr . The composition R2 R1 of R1 and R2 , i k kj m r n k R R M x y = = (( )) 1 2 1
Example: R=((a, b),(b, a),(a, c), is not symmetrIc +(c,a)→>R={(a,b),(b,a)2(a2C),(c,a)},R Is symmetric Closure
Example：R={(a,b),(b,a),(a,c)},is not symmetric + (c,a),R'={(a,b),(b,a),(a,c), (c,a)}，R' is symmetric. Closure