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This 2 page Class Notes was uploaded by Yue YU on Saturday October 24, 2015. The Class Notes belongs to CS3345 at University of Texas at Dallas taught by Yvo.Desmedt in Fall 2015. Since its upload, it has received 17 views. For similar materials see Discrete Structures in ComputerScienence at University of Texas at Dallas.
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Date Created: 10/24/15
DEFINITION 1 The universal quanti cation of P x is the statement P x for all values of x in the domain The notation VxP x denotes the universal quantification of P x Here V is called the universal quanti er We read VxP x as for all xP x or for every xP x An element for which P x is false is called a counterexample of VxP x When all the elements in the domain can be listed say x1 x2 xn it follows that the universal quantification VxP x is the same as the conjunction Pxl Px2 Pxn because this conjunction is true if and only if P x1 P x2 P xn are all true DEFINITION 2 The existential quanti cation of P x is the proposition There exists an element x in the domain such that P x We use the notation Ele x for the existential quantification of P x Here El is called the existential quantifier When all elements in the domain can be listed say x1 x2 xn the existential quantification Elex is the same as the disjunction Px1 Px2 Pxn because this disjunction is true if and only if at least one of Px1 P x2 Pxn is true TABLE 1 Erntensent When line When Feise r r is Fix is true rm ever L There is arr I re which PM is false EL Fix is an I fer whieir Pris is true Fix is false fer errerjrr s TABLE 2 Metgene fer Negn nn Equimfent Statement Is Negn en line When Feise 39e sPix r39xP s Fur energyr A Pix is false There is arr 139 tier wirieh Pix is true 39uquotr39r 3 ELFIslEl I There is an I fisr which Pix is true fer errerjrr st Pris is false TABLE 1 er 39I rre Ysriahlesi Sheernth When line iquot Elise Fs s39ajr Pis ls J39Z39lfsi Jr is true fer s1quot is There is a pair L 3 rs quotWEN Fiji 3 whieh FILL 31 is fallmi his Elr Pisa 35quot Frrr ever s there is a 1e far There is an s sueir that which Fiji y is true Pis y is false fer gee Els r39y Pisa 35quot There is err s fur wirieh PHIL 3r 1 Fur EVEIW I there is e 1e fur is true fer errer grr fr whieh FIZL y is false ElIEg1uri Jl39A i39Lsi ls There is a pair s1quot 3 Kris wirieh Pis Jr is fallse fer EljlrilsPrisi 3r Fiji Jr is THE If is