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# If A

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 = {-">-i, i}