Question

dado os conjuntos A{2,3,4,5} B{5,6,7} C{6,7} determine
a) A U(B n C)
b) A n(B U C)
c) B n(A U C)
d) (A U C) n (B U C)
e) (A U B) n (A U C)
f) (A n B) n (B n C)

Answer 1

 A  {2,3,4,5}
B   {5,6,7}
C    {6,7} 

a) A U(B n C) =  { 2,3,4,5} U { 6,7} ==> {2,3,4,5,6,7}
b) A n(B U C) = { 2 ,3,4,5} n  { 5,6,7}==> { 5 }
c) B n(A U C)  =   {5,6,7}  n  {2,3,4,5,6,7 } ==> { 5,6,7}
d) (A U C) n (B U C) =  {2,3,4,5,6,7 }  n { 5,6,7 } ==> { 5,6,7}
e) (A U B) n (A U C) = { 2,3,4,5,6,7}  n { 2,3,4,5,6,7} ==> { 2,3,4,5,6,7 }
f) (A n B) n (B n C) =   { 5 } n { 6,7 } ==> Ф

Answer 2

a)
$A\bigcup(B \bigcap C)=$

$\{2,3,4,5\}\bigcup \{6,7\}=\{2,3,4,5,6,7\}$

b)
$A\bigcap~ (B\bigcup C)= \\ \\ \{2,3,4,5\}~\bigcap~\{5,6,7\}=\{5\}$

c)
$B ~\bigcap~(A\bigcup C)= \\ \\ \{5,6,7\}~\bigcap~\{2,3,4,5,6,7\}=\{5,6,7\}$

d)
$(A\bigcup C)\bigcap~(B\bigcup C)= \\ \\ \{2,3,4,5,6,7\} \bigcap~\{5,6,7\}=\{5,6,7\}$

e)
$(A\bigcup B)~\bigcap~(A\bigcup C)= \\ \\ \{2,3,4,5,6,7\}\bigcap~\{2,3,4,5,6,7\}=\{2,3,4,5,6,7\}$

f)
$(A\bigcap B)\bigcap~(B\bigcap C)= \\ \\ \{5\}~\bigcap~\{6,7\}=\{~~~\}$