13feb-rec-parcial1.pdf - Escola Polit` ecnica Superior Grau...

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Escola Polit` ecnica Superior Universitat de Lleida Grau en Enginyeria Inform` atica ` Algebra Febrer de 2013 Recuperaci´ o Parcial 1 Problema 1. Considereu el conjunt A = { 1 , 2 , 3 , 4 } . En cadascun dels apartats seg¨uents us demanem que doneu una relaci´ o R en el conjunt A , ´ es a dir, R A × A , que satifaci unes determinades propietats. Per fer-ho, doneu el conjunt R per extensi´ o, dibuixeu el digraf associat a aquesta relaci´ o, i expliqueu detalladament perqu` e es cumpleixen cadascuna de les propietats demanades. i) Doneu una relaci´ o R que tingui 3 elements, i no sigui sim` etrica ni antisim` etrica. ii) Doneu una relaci´ o R que sigui d’equival` encia i tingui 10 elements. iii) Doneu una relaci´ o R que sigui transitiva, no-reflexiva, no-sim` etrica, no-antisim` etrica, i tingui 6 elements.
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