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ICS 241: Discrete Mathematics II (Spring 2015) Relations and Their PropertiesBinary RelationDefinition:LetA,Bbe any sets. Abinary relationRfromAtoB, writtenR:A B, is a subsetof the setA RelationDefinition:LetRbe the binary relation fromAtoB. Then the complement ofRcan be definedbyR={(a, b)|(a, b)6 R}= (A B) RInverse RelationDefinition:LetRbe the binary relation fromAtoB. Then the inverse ofRcan be defined byR 1={(b, a)|(a, b) R}Relations on a SetDefinition:Arelation on a setAis a relation fromAtoA. In other words, a relation on a setAisa subset ofA :Adirected graph, ordigraph, consists of a set V ofvertices(ornodes) together witha setEof ordered pairs of elements ofVcallededges(orarcs).
ICS 241: Discrete Mathematics II (Spring 2015) 9.1 Relations and Their Properties Binary Relation Definition: Let A, B be any sets. A binary relation R from A to B, written R : A B, is a subset
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