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Interrogation avec solution d'Algebre 1 contient ( les ensembles - les groupes -les applications ) CA$0.00
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Interrogation avec solution d'Algebre 1 contient ( les ensembles - les groupes -les applications )
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  • Course
  • Algebre 1
  • Institution
  • Ecole Nationale Polytechnique

Interrogation avec solution d'Algebre 1 contient ( les ensembles - les groupes -les applications ) ENPC_ 1er année univ

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Document information

  • April 19, 2024
  • 4
  • 2021/2022
  • Exam (elaborations)
  • Questions & answers

Subjects

  • algèbre 1
  • 1ère année universitaire

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  • Ecole Nationale Polytechnique
  • Algebre 1
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AQlàt rr-



ECOLE NATIONALE POLYTECHNIQUE CONSTANTTNE
ANNEE PR^EPARATOIRE
ALGEBRE
Interrogation 2 Durée 45 rnn
Exercice 1:
Etant donné un ensemble non vide E mcrntrer dans P(E) les égalites qui
suivent:
|-CEA L A: E,
T-CEA: E A A
.! Comparer Xtnn et Xt' XB.
Exercice 2:
1- On suppcrse que (G, *) est un groupe. I\Iontrer que la correspondance
f G -* G où /(") : z- (slrnetrique de lr pour la loi * de G) pour tout
t
élément r € G, est une application bijective.
Er,aluer f f ,G --- G.
"
2- Déterminer l'élémeut T@ * g) de G si r ei y sont deux êIénrerrt de G.
Exercice 3:
Onconsidère/: X -+ Yet g:X--+ Z devxapplicatiornetà: X --+YxZ
I'appiication caractérisée par h(r) : (/(r),9(r)) pour tout êlément r € X.
1-Evaluer h-'({y} x {r}) si g € Y et z € Z eten déduire que si / est
injective alors lz est une injection.
2- Donner une relation entre les ensembles suivants: h(A) et f (A) x g(A)
où ,4 est une partie clonnée cle X.




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