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.

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