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Let A and B be sets. The union of A and B is A U B = {x|x € A V x € B}. The intersection of A and B is A n B = {x € A A x E B}. The complement of a set A is A = {x|x € A}. Show that (A U B) = An B. Prove your result by using the definitions of union, intersection and complement of a set. Prove that (A U B) C ANB that An BC (A U B). Justify your steps. Do not use Venn Diagrams in your proof.

Let A and B be sets. The union of A and B is A U B = {x|x € A V x € B}. The intersection of A and B is A n B = {x € A A x E B}. The complement of a set A is A = {x|x € A}. Show that (A U B) = An B. Prove your result by using the definitions of union, intersection and complement of a set. Prove that (A U B) C ANB that An BC (A U B). Justify your steps. Do not use Venn Diagrams in your proof.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.1: Sets And Geometry
Problem 12E: For the sets given in Exercise 9, is there a distributive relationship for intersection with respect...
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Let A and B be sets. The union of A and B is A U B = {x|x € A V x € B}. The intersection of A and B is A n B = {x E A A x E B}. The complement of a set A is A = {x|x ¢ A}. Show that (A U B) = An B. Prove your result by using the definitions of union, intersection and complement of a set. Prove that (A U B) C AN B that An BC (A U B). Justify your steps. Do not use Venn Diagrams in your proof.
Transcribed Image Text:Let A and B be sets. The union of A and B is A U B = {x|x € A V x € B}. The intersection of A and B is A n B = {x E A A x E B}. The complement of a set A is A = {x|x ¢ A}. Show that (A U B) = An B. Prove your result by using the definitions of union, intersection and complement of a set. Prove that (A U B) C AN B that An BC (A U B). Justify your steps. Do not use Venn Diagrams in your proof.
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