SOLUTION: 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')
Algebra.Com
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.
RELATED QUESTIONS
U= {a,b,c,d,e,f,g} A={a,c,e,g,h} B={a,b,c,d} C={b,c,g,i}
(A U B') n (C n... (answered by Alan3354,MathLover1)
A’ U B’
U = {a, b, c, d, e, f, g, h, I, j, k}
A= {a, c, d, f, g, I}
B= {b, c, d, f, g}
(answered by stanbon)
• U = {a, b, c, d, e, f, g, h, i, j, k}
• A = {a, c, d, f, g, i}
• B = {b, c, d, f,... (answered by stanbon)
Determine the following: B ∪ C if:
U= {a, b, c, d, e, f, g, h, I, (answered by jim_thompson5910)
Let U ={a,b,c,d,e,f,g,h,i} be the universal set and A = {a,b,c,e}, B={c,e,d,f}, and C=... (answered by edjones)
Let U=(a,b,c,d,e,f,g,h)
A=(a,c,d)
B=(b,c,d)
C=(b,e,f,g,h)
Find the set: (answered by Edwin McCravy)
Q1) Let U={a,b,c,d,e,f,g,h,i,j},A={a,b,c,d,e},B={a,b,d,f,g},C={a,d,e} Findl... (answered by CPhill)
Set Theory
Provide answers to
B) A N C
C) AU(BNC)
D) (AUB)NC
E) A’U B’
F) (answered by jim_thompson5910)
Define sets U,A,B as shown below find (AUB)'∩ C
U=(a,b,c,d,e,f,g,h) A=(d,g,h)... (answered by Fombitz)