
 [No title] 
  Closures are also useful in reallife applications (business and social settings, transportation, etc). 
  ¡:=i¦"ª¦ óÒ¨Closures of Relations ¡$ª ¨Definition: Let R be a relation on a set A. R may or may not have some property P, such as reflexivity, symmetry, or transitivity. 
  Solution:¡@¯ "" "ª® ó¨Closures of Relations¡(ª ¨ÐExample 4 (again): Find the reflexive, symmetric and transitive closures of the relation: {(a,a), (b,b), (c,c), (a,c), (a,d), (b,d), (c,a), (d,a)} on the set S = {a,b,c,d}. 
 www.cs.umb.edu /~khsuyan/note/Session21.ppt (651 words) 
