Question:
If $A=\left\{x \in C: x^{2}=1\right\}$ and $B=\left\{x \in C: x^{4}=1\right\}$, then write $A-B$ and $B-A$.
Solution:
We have:
$A=\left\{x \in C: x^{2}=1\right\}$
$\Rightarrow A=\{-1,1\}$
And,
$B=\left\{x \in C: x^{4}=1\right\}$
$\Rightarrow \mathrm{B}=\left\{x^{4}-1=0\right\}$
$\Rightarrow \mathrm{B}=\left\{\left(x^{2}-1\right)\left(x^{2}+1\right)=0\right\}$
$\Rightarrow \mathrm{B}=\{-1,1,-\mathrm{i}, \mathrm{i}\}$
Thus, we get:
$A-B=\emptyset$
And,
B − A = {