Let A and B be sets. The union of A and B is A U B = {x|x E A V x € B}. The intersection of A and 3 is A n B = {x € A A x E B}. The complement of a set A is A = {x|x € A}. Show that AU B) = AN B. Prove your result by using the definitions of union, intersection and complement of a set. Prove that (A U B) CANB that A OBS (A U B). Justify your steps. Do not use Venn Diagrams in our proof.
Let A and B be sets. The union of A and B is A U B = {x|x E A V x € B}. The intersection of A and 3 is A n B = {x € A A x E B}. The complement of a set A is A = {x|x € A}. Show that AU B) = AN B. Prove your result by using the definitions of union, intersection and complement of a set. Prove that (A U B) CANB that A OBS (A U B). Justify your steps. Do not use Venn Diagrams in our proof.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 An B = {x E A A x € 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) CANB that AN BC (A U B). Justify your steps. Do not use Venn Diagrams in
your proof.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F191441f0-66db-457d-b504-dd20fe1485fa%2Fe9361e93-41be-4f45-bc3f-e7b067c2b5bd%2F2xd10vn_processed.jpeg&w=3840&q=75)
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 An B = {x E A A x € 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) CANB that AN BC (A U B). Justify your steps. Do not use Venn Diagrams in
your proof.
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