Question 737417: Let U = {1,2,3,4,5,6,7}
A = {1,3,5,7}
B = {1,2,3}
C = {2,3,4,5,6}
What are these sets?
2. A ∩(BUC) = {1,3,5}
4.(A∩B)U (A∩C) = {1,3,5}
6. C'∩(AUB') = {1,7}
8.(C'∩ A)U(C'∩B = {1,7}
10. (A∩B∩C)'{1,2,4,5,6,7}
12. (B U C)' ∩ A {7}
Thank you for your help in advance, means a lot, since I struggle so greatly with math. :(
Found 2 solutions by MathLover1, asaad:
Answer by MathLover1(20849)   (Show Source):
You can put this solution on YOUR website!
Let U = {1,2,3,4,5,6,7}
A = {1,3,5,7}
B = {1,2,3}
C = {2,3,4,5,6}
What are these sets?
first find (BUC)- everything that is in either of the sets
(BUC)={1,2,3,4,5,6}
(A∩B)-only the things that are in both of the sets
(A∩B)={1,3,5,7}∩{1,2,3}={1,3}
(A∩C)={1,3,5,7}∩{2,3,4,5,6}={3,5}
C'--"C' is complement", or "not C"; if U = {1,2,3,4,5,6,7} and C = {2,3,4,5,6} , then C'={1,7}
if U = {1,2,3,4,5,6,7} and B = {1,2,3}, then B'={4,5,6,7}
2. A ∩(BUC)
then
A ∩(BUC)={1,3,5,7} ∩{1,2,3,4,5,6}-only the things that are in
both of the sets
A ∩(BUC)={1,3,5}
4.(A∩B)U (A∩C)={1,3} U {3,5}={1,3,5}
6. C'∩(AUB')={1,7}∩({1,3,5,7}U{4,5,6,7} )={1,7}∩({1,3,4,5,6,7} )={1,7}
8.(C'∩ A)U(C'∩B')=({1,7}∩{1,3,5,7})U({1,7}∩{4,5,6,7})=({1,7})U ({7})={1,7}
10. (A∩B∩C)'=({1,3,5,7}∩ {1,2,3} ∩{2,3,4,5,6})'=(1,3}∩{2,3,4,5,6})'=(3)'= {1,2,4,5,6,7}
12. (B U C)' ∩ A=({1,2,3}U{2,3,4,5,6})'∩ {1,3,5,7}=({1,2,3,4,5,6})'∩ {1,3,5,7}={2,4,6}
Answer by asaad(2)  (Show Source):
You can put this solution on YOUR website!
2. A ∩(BUC) = {1,3,5}
4.(A∩B)U (A∩C) = {1,3,5}
6. C'∩(AUB') = {1,7}
8.(C'∩ A)U(C'∩B = {1,7}
10. (A∩B∩C)' ={1,2,4,5,6,7}
12. (B U C)' ∩ A = {7}
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