21-SetOpsTupsRels

21-SetOpsTupsRels - Discussion#21 Sets Set Operations...

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1 Discussion #21 Discussion #21 Tuples & Relations

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2 Discussion #21 Topics Sets and Set Operations Definitions Operations Set Laws Derivations, Equivalences, Proofs Tuples and Relations Tuples Cartesian Product Relations subset of the cross product
3 Discussion #21 Sets Sets are collections The things in a collection are called elements or members Sets have no duplicates. Notation { } Enumerate: {1, 2, 3} Ellipsis: {1, 2, …} or {1, 2, … , 100} Universe: All elements under consideration. E (in our text) more common: U for Universe of Discourse Empty set: { } or i.e. set with no elements Special sets N natural numbers {0, 1, 2, …} (some exclude 0 from this set) Z integers; R reals “set builder” notation { x | P(x)} all elements in E that satisfy predicate P { x | x>5 x<10} = {6, 7, 8, 9} when E = N Element of: x A Cardinality |A| or #A both denote the number of elements in A, e.g. |{a,b}| = 2

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4 Discussion #21 Set Equality, Subsets, Supersets Set Equality A = B if A and B have the same elements A = B x A x B Subsets A B x A x B (subset or equal) A B A B 5 x(x B x A) (proper subset) Supersets A B if B A A B if B A
5 Discussion #21 Proofs about Set Equality and the Empty Set Prove: A = B iff A B B A A = B x A x B

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21-SetOpsTupsRels - Discussion#21 Sets Set Operations...

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