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Lecture Notes for CMSC 250 - Discrete Structures with Plane at Maryland (UMD)

Notes Information

Material Type:Class Note
Professor:Plane
Class:CMSC 250 - Discrete Structures
Subject:Computer Science
University:University of Maryland
Term:Fall 2006
Keywords:
  • Cartesian Product
  • Definitions
  • Venn Diagrams
  • Combinations
  • Infinite Sets
  • Relationship
  • Intersection
  • Propositional
  • Transitivity
  • Introduction
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Sets Definition of a Set: NAME = {list of elements or description of elements} i.e. B = {1,2,3} or C = {x?Z + | -4 < x < 4} Axiom of Extension: A set is completely defined by its elements i.e. {a,b} = {b,a} = {a,b,a} = {a,a,a,b,b,b} Subset A?B ??x?U, x?A?x?B A is contained in B B contains A A? B ??x ?U, x?A ^ x?B Relationship between membership and subset: ?x?U, x?A ? {x} ? A Definition of set equality: A = B ? A? B ^ B? A Same Set or Not?? X={x?Z | ?p ?Z, x = 2p} Y={y?Z | ?q?Z, y = 2q-2} A={x?Z | ?i ?Z, x = 2i+1} B={x?Z | ?i ?Z, x = 3i+1} C={x?Z | ?i ?Z, x = 4i+1} Set Operations Formal Definitions and Venn Diagrams Union: Intersection: Complement: Difference: }|{ BxAxUxBA ????=U }|{ BxAxUxBA ????=I }|{ BxAxUxBA ????=? }|{' AxUxAA c ??== 'BABA I=? Ordered n-tuple and the Cartesian Product . Ordered n-tuple - takes order and multiplicity into account .(x 1 ,x 2 ,x 3 ,.,x n ) - n values - not necessarily distinct - in the order given .(x 1 ,x 2 ,...

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