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[{"id":51451,"question":"Quel symbole représente l'appartenance d'un élément à un ensemble ?","option_a":"∈","option_b":"⊂","option_c":"⊄","option_d":"⊆","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le symbole ∈ signifie 'appartient à'. Par exemple, 5 ∈ {1, 5, 9} se lit '5 appartient à l'ensemble {1, 5, 9}'.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51452,"question":"Si A = {1, 2, 3} et B = {3, 4, 5}, que vaut A ∩ B ?","option_a":"{1, 2, 3, 4, 5}","option_b":"{3}","option_c":"{1, 2, 4, 5}","option_d":"∅","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'intersection A ∩ B contient uniquement les éléments communs aux deux ensembles, ici {3}.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51453,"question":"Vrai ou Faux ? L'ensemble vide est un sous-ensemble de tout ensemble.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'ensemble vide (∅) est inclus dans tous les ensembles, car il n'a aucun élément qui pourrait 'sortir' des conditions d'inclusion.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51454,"question":"Quelle opération donne tous les éléments présents dans A ou B, mais pas dans les deux ?","option_a":"A ∪ B","option_b":"A ∩ B","option_c":"A \\ B","option_d":"A Δ B","option_e":"","option_f":"","bonne_reponse":"D","explication":"La différence symétrique (Δ) entre A et B donne les éléments qui sont dans A ou B, mais pas dans les deux simultanément.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51455,"question":"Si A = {x ∈ ℕ | x est pair}, quel est le complémentaire de A dans ℕ ?","option_a":"{x ∈ ℕ | x est impair}","option_b":"{0, 2, 4, 6, ...}","option_c":"ℕ","option_d":"∅","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le complémentaire de A dans ℕ regroupe tous les entiers naturels qui ne sont pas pairs, c'est-à-dire les entiers impairs.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51456,"question":"Vrai ou Faux ? Pour tous ensembles A et B, A ∪ B = B ∪ A.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'union est commutative : l'ordre des ensembles n'a pas d'importance dans A ∪ B.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51457,"question":"Quel est le résultat de {1, 2} ∪ {2, 3} ?","option_a":"{1, 2, 3}","option_b":"{2}","option_c":"{1, 3}","option_d":"∅","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'union de {1, 2} et {2, 3} regroupe tous les éléments distincts des deux ensembles : {1, 2, 3}.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51458,"question":"Vrai ou Faux ? Si A ⊂ B, alors A ∩ B = A.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Si A est un sous-ensemble de B, alors tous les éléments de A sont aussi dans B. Ainsi, A ∩ B = A.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51459,"question":"Quelle propriété est illustrée par (A ∪ B) ∩ C = (A ∩ C) ∪ (B ∩ C) ?","option_a":"Commutativité","option_b":"Associativité","option_c":"Distributivité","option_d":"Idempotence","option_e":"","option_f":"","bonne_reponse":"C","explication":"Cette égalité illustre la distributivité de l'intersection sur l'union.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51460,"question":"Quel ensemble représente {x ∈ ℝ | x² = 4} ?","option_a":"{2}","option_b":"{-2, 2}","option_c":"{0, 2}","option_d":"ℝ","option_e":"","option_f":"","bonne_reponse":"B","explication":"Les solutions réelles de x² = 4 sont x = -2 et x = 2, donc l'ensemble est {-2, 2}.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]