Question

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

Answer 1

Given: $A=\{1,2,3,4\}B=\{3,4,5,6\},$
$C=\{5,6,7,8\}$and $D=\{7,8,9,10\}$

$A\cup B=\{1,2,3,4\}\cup \{3,4,5,6\}$
Hence, $A\cup B=\{1,2,3,4,5,6\}$

$A\cup C=\{1,2,3,4\}\cup \{5,6,7,8\}$
Hence, $A\cup C$ = {1,2,3,4,5,6,7,8}

$B\cup C=\{3,4,5,6\}\cup \{5,6,7,8\}$
Hence, $B\cup C=\{3,4,5,6,7,8\}$

$B\cup D=\{3,4,5,6\}\cup \{7,8,9,10\}$
Hence, $B\cup D=\{3,4,5,6,7,8,9,10\}$

$\because A\cup B=\{1,2,3,4,5,6\}$
$\therefore A\cup B\cup C=\{1,2,3,4,5,6\}\cup \{5,6,7,8\}$
Hence, $A\cup B\cup C=\{1,2,3,4,5,6,7,8\}$

$\because A\cup B=\{1,2,3,4,5,6\}$
$\therefore A\cup B\cup D=\{1,2,3,4,5,6\}\cup \{7,8,9,10\}$
Hence, $A\cup B\cup D=\{1,2,3,4,5,6,7,8,9,10\}$

$B\cup C=\{3,4,5,6,7,8\}$
$\therefore B\cup C\cup D=\{3,4,5,6,7,8\}\cup \{7,8,9,10\}$
Hence, $B\cup C\cup D=\{3,4,5,6,7,8,9,10\}$