# 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 2005 Keywords: Cartesian ProductDefinitionsVenn DiagramsCombinationsInfinite SetsRelationshipIntersectionPropositionalTransitivityIntroduction      ## 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,...

## Related Documents Definitions Notes Rational Number Quiz Square Brackets Quiz Square Brackets Quiz Square Brackets Quiz Cmsc 250 Quiz Quiz Square Brackets Quiz Square Brackets Quiz Square Brackets Quiz Bijective Function Notes Square Brackets Quiz Either...or Quiz Make-to-Order Quiz Combinations Quiz Square Brackets Quiz Square Brackets Quiz