Question

If $A=\{xϵC:x^2=1\}$ and $B=\{xϵC:x^4=1\}$, then $A\Delta B$ is equal to

• A. $\{-1,1\}$
• B. $\{-1,1,i,-i\}$
• C. $\{-i,i\}$
• D. None of these

Answer 1

Answer: (C)

$\{-i,i\}$

$x^2=1\Rightarrow x=-1,1.\therefore A=\{-1,1\}$
$x^4=1\Rightarrow x^2=-1,1$
$\Rightarrow x=-i,i,-1,1.\therefore B=\{-i,i,-1,1\}$
$\therefore A\Delta B=(A-B)\cup (B-A)=\varphi \cup \{-i,i\}=\{-i,i\}$.