relations and functions pdf

endstream endobj 86 0 obj <> endobj 92 0 obj <>/ExtGState<>/Font<>/ProcSet[/PDF/Text/ImageC/ImageI]/XObject<>>>/Rotate 0/Type/Page>> endobj 1 0 obj <>/ExtGState<>/Font<>/ProcSet[/PDF/Text]/XObject<>>>/Rotate 0/Type/Page>> endobj 5 0 obj <>/ExtGState<>/Font<>/ProcSet[/PDF/Text]/XObject<>>>/Rotate 0/Type/Page>> endobj 7 0 obj <>/ExtGState<>/Font<>/ProcSet[/PDF/Text]/XObject<>>>/Rotate 0/Type/Page>> endobj 9 0 obj <>/ExtGState<>/Font<>/ProcSet[/PDF/Text]/XObject<>>>/Rotate 0/Type/Page>> endobj 11 0 obj <>/ExtGState<>/Font<>/ProcSet[/PDF/Text]/XObject<>>>/Rotate 0/Type/Page>> endobj 13 0 obj <>/ExtGState<>/Font<>/ProcSet[/PDF/Text]/XObject<>>>/Rotate 0/Type/Page>> endobj 15 0 obj <>/ExtGState<>/Font<>/ProcSet[/PDF/Text]/XObject<>>>/Rotate 0/Type/Page>> endobj 17 0 obj <>/ExtGState<>/Font<>/ProcSet[/PDF/Text]/XObject<>>>/Rotate 0/Type/Page>> endobj 19 0 obj <>/ExtGState<>/Font<>/ProcSet[/PDF/Text]/XObject<>>>/Rotate 0/Type/Page>> endobj 21 0 obj <>/ExtGState<>/Font<>/ProcSet[/PDF/Text]/XObject<>>>/Rotate 0/Type/Page>> endobj 23 0 obj <>/ExtGState<>/Font<>/ProcSet[/PDF/Text]/XObject<>>>/Rotate 0/Type/Page>> endobj 26 0 obj <>/ExtGState<>/Font<>/ProcSet[/PDF/Text]/XObject<>>>/Rotate 0/Type/Page>> endobj 35 0 obj <>/ExtGState<>/Font<>/ProcSet[/PDF/Text]/XObject<>>>/Rotate 0/Type/Page>> endobj 37 0 obj <>/ExtGState<>/Font<>/ProcSet[/PDF/Text]/XObject<>>>/Rotate 0/Type/Page>> endobj 39 0 obj <>/ExtGState<>/Font<>/ProcSet[/PDF/Text]/XObject<>>>/Rotate 0/Type/Page>> endobj 41 0 obj <>/ExtGState<>/Font<>/ProcSet[/PDF/Text]/XObject<>>>/Rotate 0/Type/Page>> endobj 43 0 obj <>/ExtGState<>/Font<>/ProcSet[/PDF/Text]/XObject<>>>/Rotate 0/Type/Page>> endobj 45 0 obj <>/ExtGState<>/Font<>/ProcSet[/PDF/Text]/XObject<>>>/Rotate 0/Type/Page>> endobj 193 0 obj <>stream Show that R is an equivalence relation. 0000007291 00000 n 0000000016 00000 n endobj 4 CS 441 Discrete mathematics for CS M. Hauskrecht Relations and functions • Relations represent one to many relationships between elements in A and B. endobj 112 39 0000006586 00000 n We do this as follows: 1. 150 0 obj<>stream 38 0 obj << /S /GoTo /D (section*.12) >> stream 0000027523 00000 n B. 0000001076 00000 n uuid:26a83948-ce13-49ed-bdca-f2c314599c8b 0000020643 00000 n 1. 14 0 obj endobj 0000012617 00000 n endobj %PDF-1.4 %���� 2017-11-03T11:55:23 0000014353 00000 n acer endobj (\376\377\000C\000o\000u\000n\000t\000i\000n\000g\000\040\000R\000e\000l\000a\000t\000i\000o\000n\000s) Sets of ordered-pair numbers can represent relations or functions. (\376\377\000E\000q\000u\000i\000v\000a\000l\000e\000n\000c\000e\000\040\000R\000e\000l\000a\000t\000i\000o\000n\000s) 26 0 obj >> Ling 310, adapted from UMass Ling 409, Partee lecture notes March 1, 2006 p. 1 Set Theory Basics.doc Basic Concepts of Set Theory, Functions and Relations endobj << /S /GoTo /D (subsection*.10) >> 0000006133 00000 n %%EOF 30 0 obj (\376\377\000P\000r\000o\000b\000l\000e\000m\000s\000\040\000o\000n\000\040\000L\000o\000g\000a\000r\000i\000t\000h\000m\000s\000\040\000a\000n\000d\000\040\000E\000x\000p\000o\000n\000e\000n\000t\000i\000a\000l\000s) 0000020410 00000 n 0000011596 00000 n 0000005206 00000 n For example, (4, 7) is an ordered-pair number; the order is designated by the first element 4 and the second element 7. endobj 34 0 obj xref 0000002320 00000 n 22 0 obj 43 0 obj H��W�r�8}gU������F\fk'�Lf��YkkR��ڢeJb"���'���h����(��}X�bC�8}����|Q��1�1z��%�*z:e��Đ�qn�3iΧ`V0���Ă�7��Y��4qs�Ǻ���~�N���:�a���+7�r�K�Dl8�[�9%�u���^^jru�.�䞠k�=a\�Ut�:�A�22�� &���Qz�����0� 6Ә%�K=�ǵ&�r[NX"ђ���ɢ�w�2��`�R�,Nyl ��H���� acLa��Ѱ1�h?�� Functions A function is a relation that satisfies the following: each -value is allowed onlyone -value Note: (above) is not a function, because has -values and (violates our condition!)

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