# Lesson 19.docx - Discrete Mathematics Lesson 19 Page 1 of 6...

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Discrete MathematicsLesson 19Page1of6Discrete MathematicsLesson 19 – Setsin late nineteenth century, Georg Cantor was first to realize potential usefulness of investigatingproperties in setsabstract set theory regarded as foundation of mathematical thoughtall mathematical objects can be defined in terms of setslanguage of set theory used in every mathematical subjectwordssetandelementundefined terms of set theoryolikesentence,true,falseare undefined terms of logicCantor suggested imagining set as a “collection into a wholeMof definite and separate objectsof our intuition or our thought.These objects are called the elements ofM.”letSdenote a set andaan element ofSoaSmeansais an element ofSoaSmeansais not an element ofSoifSis a set andP xis a property that elements ofSmay or may not satisfy, thenAmay be defined by writing:APxSx, read “the set of allxinSsuch thatPofx.”Definition 1IfAandBare sets, thenAis called asubsetofB, writtenAB, if and only if everyelement ofAis also an element ofB.The phrasesA is contained in BandB contains Aare alternative

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