Logique et Ensembles : Testez vos connaissances en Mathématiques

Question 1 sur 10 10:00

[{"id":54951,"question":"Quelle est la négation de la proposition 'P ET Q' ?","option_a":"NON P ET NON Q","option_b":"NON P OU NON Q","option_c":"P OU Q","option_d":"P ET NON Q","option_e":"","option_f":"","bonne_reponse":"B","explication":"La négation de 'P ET Q' est 'NON P OU NON Q' d'après les lois de De Morgan.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":54952,"question":"Soit A = {1, 2, 3} et B = {2, 3, 4}. Quelle est A ∩ B ?","option_a":"{1, 2, 3, 4}","option_b":"{2, 3}","option_c":"{1, 4}","option_d":"∅","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'intersection A ∩ B est l'ensemble des éléments communs à A et B, soit {2, 3}.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":54953,"question":"Une fonction f est injective si et seulement si :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une fonction est injective si deux éléments distincts de l'ensemble de départ ont toujours des images distinctes dans l'ensemble d'arrivée.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":54954,"question":"Quelle est la valeur de vérité de la proposition 'Si 2+2=5 alors Paris est la capitale de la Tunisie' ?","option_a":"Vrai","option_b":"Faux","option_c":"Indéterminé","option_d":"Ni vrai ni faux","option_e":"","option_f":"","bonne_reponse":"A","explication":"En logique, une implication est vraie si l'antécédent est faux, quelle que soit la conséquence.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":54955,"question":"Soit E = {x ∈ ℕ | x est pair}. Quel est le complémentaire de E dans ℕ ?","option_a":"{x ∈ ℕ | x est impair}","option_b":"{0}","option_c":"ℕ","option_d":"∅","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le complémentaire de l'ensemble des nombres pairs dans ℕ est l'ensemble des nombres impairs.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":54956,"question":"La proposition 'Pour tout x ∈ ℝ, x² ≥ 0' est :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le carré de tout nombre réel est toujours positif ou nul.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":54957,"question":"Soit f(x) = 2x + 1. Quelle est l'image de 3 par f ?","option_a":"5","option_b":"7","option_c":"6","option_d":"4","option_e":"","option_f":"","bonne_reponse":"B","explication":"f(3) = 2*3 + 1 = 7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":54958,"question":"La fonction f(x) = x² est :","option_a":"Injective","option_b":"Non injective","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction carrée n'est pas injective car f(2) = f(-2) = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":54959,"question":"Quelle est la table de vérité de 'P ⇒ Q' ?","option_a":"\u003Ctable\u003E...\u003C\/table\u003E","option_b":"Vrai seulement si P et Q sont vrais","option_c":"Faux seulement si P est vrai et Q est faux","option_d":"Vrai dans tous les cas sauf quand P et Q sont faux","option_e":"","option_f":"","bonne_reponse":"C","explication":"L'implication 'P ⇒ Q' est fausse uniquement lorsque P est vrai et Q est faux.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":54960,"question":"Soit A = {1, 2, 3} et B = {4, 5}. Quelle est A ∪ B ?","option_a":"{1, 2, 3, 4, 5}","option_b":"{1, 2, 3}","option_c":"{4, 5}","option_d":"∅","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'union A ∪ B est l'ensemble de tous les éléments appartenant à A ou à B, soit {1, 2, 3, 4, 5}.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]