Question

If $\xi$ = {$a,b,c,d,e,f,g,h$}, $A=$ {$b,c,d,e,f$}, $B=$ {$a,b,c,g,h$} and $C=$ {$c,d,e,f,g$},

then (B - C)${}^{\prime }$ = C${}^{\prime }$ - B${}^{\prime }$ is,

• A. True
• B. False

Answer 1

The correct option is B False

Given, $\xi$ = {$a,b,c,d,e,f,g,h$}, $A=$ {$b,c,d,e,f$}, $B=$ {$a,b,c,g,h$} and $C=$ {$c,d,e,f,g$}

$B-C$ will have elements of $B$ which are not in $C$
So, $B-C=$ { $a,b,h$ }
And ${(B-C)}^{{}^{\prime }}=\xi -(B-C)=$ { $c,d,e,f,g$ } .....(1)
Also, $C^{{}^{\prime }}=\xi -C=$ { $a,b,h$ }
$B^{{}^{\prime }}=\xi -B=$ { $d,e,f$ }
$C^{{}^{\prime }}-B^{{}^{\prime }}$ will have elements of $C^{{}^{\prime }}$ which are not in $B^{{}^{\prime }}$
And, $C^{{}^{\prime }}-B^{{}^{\prime }}=$ { $a,b,h$ } ....(2)
From (1) and (2) we have,
${(B-C)}^{{}^{\prime }}\ne C^{{}^{\prime }}-B^{{}^{\prime }}$