Question

If $U=\{a,b,c,d,e,f,g,h\},$ find the complements of following sets:
$\left(i\right)A=\{a,b,c\}\left(ii\right)B=\{d,e,f,g\}$
$\left(iii\right)C=\{a,c,e,g\}\left(iv\right)D=\{f,g,h,a\}$

Answer 1

$\left(i\right)$ Given, $U=\{a,b,c,d,e,f,g,h\}$ and $A=\{a,b,c\}$
$\because A^{\prime }=U-A$
$\Rightarrow A^{\prime }=\{a,b,c,d,e,f,g,h\}-\{a,b,c\}$
$\Rightarrow A^{\prime }=\{d,e,f,g,h\}$

$\left(ii\right)$ Given: $U=\{a,b,c,d,e,f,g,h\}$ and $B=\{d,e,f,g\}$
$\because B^{\prime }=U-B$
$\Rightarrow B^{\prime }=\{a,b,c,d,e,f,g,h\}-\{d,e,f,g\}$
$\Rightarrow B^{\prime }=\{a,b,c,h\}$

$\left(iii\right)$ Given $U=\{a,b,c,d,e,f,g,h\}$ and $C=\{a,c,e,g\}$
$\because C^{\prime }=U-C$
$\Rightarrow C^{\prime }=\{a,b,c,d,e,f,g,h\}-\{a,c,e,g\}$
$\Rightarrow C^{\prime }=\{b,d,f,h\}$

$\left(i\right)$ Given: $U=\{a,b,c,d,e,f,g,h\}$ and $D=\{f,g,h,a\}$
$\because D^{\prime }=U-D$
$\Rightarrow D^{\prime }=\{a,b,c,d,e,f,g,h\}-\{f,g,h,a\}$
$\Rightarrow D^{\prime }=\{b,c,d,e\}$