Question 1190043: 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}
(A U B') n (C n B')
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
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' = {a,b,c,d,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'
A = {a,c,g,h}
B' = {e,f,g,h,i}
A u B' = {a,c,g,h e,f,g,h,i}
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 = {g,i} is the final answer
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.
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