Quiz — Applications et parties d’un ensemble, II.pdf

Question 1 sur 10 20:00

[{"id":94744,"question":"Soit un ensemble E = {1, 2, 3}. Combien de parties contient-il ?","option_a":"3","option_b":"6","option_c":"8","option_d":"9","option_e":"","option_f":"","bonne_reponse":"c","explication":"Un ensemble à n éléments a 2^n parties. Ici, E a 3 éléments, donc 2^3 = 8 parties.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"3\", \"b\": \"6\", \"c\": \"8\", \"d\": \"9\"}}","_debug_options_count":4},{"id":94745,"question":"Une application peut-elle associer deux éléments différents du même ensemble ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Non, une application associe à chaque élément d’un ensemble un unique élément d’un autre ensemble.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":94746,"question":"Quel est le nombre de parties d’un ensemble à 4 éléments ?","option_a":"8","option_b":"12","option_c":"16","option_d":"32","option_e":"","option_f":"","bonne_reponse":"d","explication":"Un ensemble à 4 éléments a 2^4 = 16 parties.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"8\", \"b\": \"12\", \"c\": \"16\", \"d\": \"32\"}}","_debug_options_count":4},{"id":94747,"question":"Soit A = {a, b} et B = {1, 2}. Combien d’applications existe-t-il de A vers B ?","option_a":"2","option_b":"4","option_c":"8","option_d":"16","option_e":"","option_f":"","bonne_reponse":"b","explication":"Pour chaque élément de A, il y a 2 choix dans B. Donc 2^2 = 4 applications possibles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"2\", \"b\": \"4\", \"c\": \"8\", \"d\": \"16\"}}","_debug_options_count":4},{"id":94748,"question":"L’ensemble vide est-il une partie de tout ensemble ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Oui, l’ensemble vide est toujours une partie de tout ensemble.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":94749,"question":"Soit E = {x, y, z}. Quelle est la partie {x, y} ?","option_a":"Un sous-ensemble de E","option_b":"Un élément de E","option_c":"Un ensemble vide","option_d":"Une application","option_e":"","option_f":"","bonne_reponse":"a","explication":"{x, y} est un sous-ensemble de E car tous ses éléments appartiennent à E.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Un sous-ensemble de E\", \"b\": \"Un élément de E\", \"c\": \"Un ensemb","_debug_options_count":4},{"id":94750,"question":"Une application injective associe des éléments distincts à des éléments distincts.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Oui, une application injective (ou biunivoque) associe des éléments distincts à des éléments distincts.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":94751,"question":"Soit A = {1, 2} et B = {3, 4, 5}. Combien d’applications existe-t-il de B vers A ?","option_a":"4","option_b":"6","option_c":"8","option_d":"9","option_e":"","option_f":"","bonne_reponse":"d","explication":"Pour chaque élément de B, il y a 2 choix dans A. Donc 2^3 = 8 applications possibles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"4\", \"b\": \"6\", \"c\": \"8\", \"d\": \"9\"}}","_debug_options_count":4},{"id":94752,"question":"L’ensemble des parties d’un ensemble E est noté comment ?","option_a":"P(E)","option_b":"E²","option_c":"2E","option_d":"∅(E)","option_e":"","option_f":"","bonne_reponse":"a","explication":"L’ensemble des parties d’un ensemble E est noté P(E).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"P(E)\", \"b\": \"E²\", \"c\": \"2E\", \"d\": \"∅(E)\"}}","_debug_options_count":4},{"id":94753,"question":"Une application peut-elle être à la fois injective et surjective ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Oui, une application qui est à la fois injective et surjective est appelée une bijection.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4}]