# 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 2004 Keywords: DefinitionsVenn DiagramsCombinationsInfinite SetsCartesian ProductRelationshipIntersectionPropositionalTransitivityIntroduction      ## Sample Document Text

1 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?Afix?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 2 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 ? ??= }|{ BxAxUxBA ? ??= }|{ BxAxUxBA ? ??=- }|{' AxUxAAc ??== 'BABA =- 3 Ordered n-tuple and the Cartesian Product . Ordered n-tuple - takes order and multiplicity into account . (x1,x2,x3,.,xn) - n values - not necessarily distinct - in the order given . (x1,x2,x3,.,xn) = (y1,...

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