Answer
{1,3,4,6}
Work Step by Step
(A U B) ∩ C
We start by doing what is in the parentheses: A U B.
A U B means the union of all of the elements in sets A and B.
A={1,3,4,5,9}
B={2,4,6,7,8}
If we put together the elements of both sets we get: 1,3,4,5,9 and 2,4,6,7,8.
Next we should remove any duplicates: 4 is the only duplicate in that case
Now we have 1,3,4,5,9 and 2,6,7,8
Putting them in order for readability we have A U B= {1,2,3,4,5,6,7,8,9}
Now we need to find the intersection of that set with set C:
{1,2,3,4,5,6,7,8,9} ∩ C
C={1,3,4,6}
So we have
{1,2,3,4,5,6,7,8,9} ∩ {1,3,4,6}.
By intersection we mean those elements that are in both sets . That is the elements must be in both sets to be in the intersection. Set C is smaller so I would compare each of those elements with the elements in the first set (AUB).
Note 1, is in both sets. So are the numbers 3,4, and 6. So all of the elements of C are in the intersection. Nothing else can be in the intersection because it isn’t in C.
The final answer is {1,3,4,6}.
