Question 1190043
<font color=black size=3>
Universal set = U = {a,b,c,d,e,f,g,h,i}
A = {a,c,g,h}
B = {a,b,c,d}
C = {b,c,g,i}


B' = set of everything NOT in set B
B' = {<s>a,b,c,d</s>,e,f,g,h,i}
B' = {e,f,g,h,i}
I started with the universal set, then crossed off stuff I found in set B
An item is either in set B, or it is in set B', but not both sets at once.


Let's union sets A and B'
<font color=blue>A = {a,c,g,h}</font>
<font color=red>B' = {e,f,g,h,i}</font>
<font color=blue>A</font> u <font color=red>B'</font> = {<font color=blue>a,c,g,h</font>    <font color=red>e,f,g,h,i</font>}
A u B' = {a,c,e,f,g,h,i}
As the third step shows, I simply glued the two sets together to form a larger one. The color coding shows where the items are coming from. Then I sorted the items and tossed any duplicates.


Next, we'll intersect sets C and B'
C = {b,c,g,i}
B' = {e,f,g,h,i}
C n B' = {g,i}
This is the set of items found in BOTH C and B'


The last step is to intersect the two results from each previous section
D = A u B' = {a,c,e,f,g,h,i}
E = C n B' = {g,i}
D n E = (A u B') n (C n B')
D n E = <font color=red>{g,i} is the final answer</font>


Side note: be sure to not mix up the notation for the union symbol and the universal set. I decided to go with lowercase 'u' to represent the union symbol, and uppercase U to represent the universal set. The n refers to the intersection symbol.
</font>