Question 29712: Given U = {1,2,3,4,5,6,7,8,9,10}, A ={1,2,3}, and B = {3,6,9}, find the complement of A U B.
A. 3
B. {4,5,7,8,10}
C. {1,2,4,5,6,7,8,9,10}
D. {1,2,3,4,5,6,7,8,9,10}
Answer by sdmmadam@yahoo.com(530)   (Show Source):
You can put this solution on YOUR website!Given U = {1,2,3,4,5,6,7,8,9,10}, A ={1,2,3}, and B = {3,6,9}, find the complement of A U B.
U = {1,2,3,4,5,6,7,8,9,10}, A ={1,2,3}, and B = {3,6,9}
A U B is made of all elements of A and all elements of B (one element taken only once)
Therefore A U B = {1,2,36,9}
The complemnet of A U B in U means the set of all those elements of U after removing the elements of AUB from U
complement of A U B = {4,5,7,8,10}
which is your choice B.
What is the verification?
The UNION of the complement of a set in U and the set
should give the whole set U back.
Ofcourse the answer set(that is the complement set) and the set (AUB) give their union equal to U itself .
[complement of A U B]U(AUB)
= {4,5,7,8,10}U {1,2,36,9}
={1,2,3,4,5,6,7,8,9,10}
=U
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