Let U={1,2,3,4,5,6}, A={1,3,5}, B={2,4,5,6}, and C={1,2,4,6}. Find:
1.A' union B
2. A union B'
3. A' intersection B
4. A intersection B'
5. A' intersection C
6. A intersection C'
7. (A intersection C)'
8. (A union B)'
9. (A intersection B)'
10. (A intersection C)' union B

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union of a and b{1,3,5,2,4,6} intersection of a and b {5} a and c {1} intersection of a and c {1.2.4.5,6}

Answers

2014-06-29T13:47:38+08:00
1.) A' U B = A'= {2,4,6} = {2,4,5,6}
2.) A U B' = B'= 
{1,3} = {1,3,5}
3.) A' intersection B =  
{2,4,6} = {2,4,6}
4.) A intersection B' =
{1,3} = {1,3}
5.) A' intersection C =
{2,4,6} = {2,4,6}
6.) A intersection C' = C'= 
{3,5} = {3,5}
7.) (A intersection C)' = 
{1} = {2,4,5,6}
8.) (A U B)' = {1,2,3,4,5,6}  = { } or null set
9.) 
 (A intersection B)' = {5}  = {1,2,3,4,6}
10.) (A intersection C)' U B = {1}  = {2,3,4,5,6}  = {2,3,4,5,6}
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