Question

If $A=\{x:x^2=1\}andB=\{x:x^4=1\}$ then $A△B$is equal to

Answer 1

Finding the value of $A△B$:

Given $A=\{x:x^2=1\}andB=\{x:x^4=1\}$

$$\begin{gathered} A=\{x:x^2=1\} \\ {x}^2=1 \\ x=\pm 1 \\ A=\{-1,1\} \\ B=\{x:x^4=1\} \\ {x}^4=1 \\ {x}^2=\pm 1 \\ {x}^2=1 \\ x=\pm 1 \\ {x}^2=-1 \\ x=\pm i \\ B=\{1,–1,i,-i\} \\ A△B=(A–B)\cup (B–A) \\ =ɸ\cup \{i,-i\} \\ A△B=\{i,-i\} \end{gathered}$$

Hence, the value of $A△B$is $\{i,-i\}$