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If $A=\{1,2,3,4\}, B=\{3,4,5,6\}, C=\{5,6,7,8\}$ and $D=\{7,8,9,10\}$; find
(i) $A \cup B$
(ii) $A \cup C$
(iii) $B \cup C$
(iv) $B \cup D$
(v) $A \cup B \cup C$
(vi) $A \cup B \cup D$
(vii) $B \cup C \cup D$.
(i) $A \cup B$
(ii) $A \cup C$
(iii) $B \cup C$
(iv) $B \cup D$
(v) $A \cup B \cup C$
(vi) $A \cup B \cup D$
(vii) $B \cup C \cup D$.
Solution:
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Verified Answer
(i) $A \cup B=\{1,2,3,4\} \cup\{3,4,5,6\}$
$=\{1,2,3,4,5,6\}$
(ii) $A \cup C=\{1,2,3,4\} \cup\{5,6,7,8\}$
$=\{1,2,3,4,5,6,7,8\}$
(iii) $B \cup C=\{3,4,5,6\} \cup\{5,6,7,8\}$
$=\{3,4,5,6,7,8\}$
(iv) $B \cup D=\{3,4,5,6\} \cup\{7,8,9,10\}$
$=\{3,4,5,6,7,8,9,10\}$
(v) $A \cup B \cup C$
$=\{1,2,3,4\} \cup\{3,4,5,6\} \cup\{5,6,7,8\}$
(vi) $A \cup B \cup D$
$=\{1,2,3,4\} \cup\{3,4,5,6\} \cup\{7,8,9,10\}$
$=\{1,2,3,4,5,6,7,8,9,10\}$
(vii) $B \cup C \cup D$
$=\{3,4,5,6\} \cup\{5,6,7,8\} \cup\{7,8,9,10\}$
$=\{3,4,5,6,7,8,9,10\} .$
$=\{1,2,3,4,5,6\}$
(ii) $A \cup C=\{1,2,3,4\} \cup\{5,6,7,8\}$
$=\{1,2,3,4,5,6,7,8\}$
(iii) $B \cup C=\{3,4,5,6\} \cup\{5,6,7,8\}$
$=\{3,4,5,6,7,8\}$
(iv) $B \cup D=\{3,4,5,6\} \cup\{7,8,9,10\}$
$=\{3,4,5,6,7,8,9,10\}$
(v) $A \cup B \cup C$
$=\{1,2,3,4\} \cup\{3,4,5,6\} \cup\{5,6,7,8\}$
(vi) $A \cup B \cup D$
$=\{1,2,3,4\} \cup\{3,4,5,6\} \cup\{7,8,9,10\}$
$=\{1,2,3,4,5,6,7,8,9,10\}$
(vii) $B \cup C \cup D$
$=\{3,4,5,6\} \cup\{5,6,7,8\} \cup\{7,8,9,10\}$
$=\{3,4,5,6,7,8,9,10\} .$
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