Answer:
We have:
A={1,3,6,8,9,12,15}
B={6,9,12}
Let's analyze the statements:
1) B is the complement of A:
The complement of a set W is the set with all the elements in the universal set that do not belong to the set W, in this case, you can see that the 3 elements of set B do also belong to set A, then this statement is false.
2) A and B are disjoint sets:
Two sets are disjoint if they do not share any element, in this case, the 3 elements of B also belong to A, then the sets share elements, which means that the sets are not disjoint, so this statement is false.
3) A∩B=∅
A∩B is the set of all the common elements of A and B, in this case we have:
A∩B = {6, 9, 12}
Then the statement is false.
4) BUA = A
BUA is the union of set A and B, and it's defined as the combination of all elements of A and B (such that there are no repeated elements)
Or we can write this as:
A + B - A∩B = {6,9,12} + {1,3,6,8,9,12,15} - {6,9,12}
= {1,3,6,8,9,12,15} = A
Then BUA = A
This is true.