Question

What is the symmetric difference of two sets $A$ and $B$?

Answer 1

Explain the symmetric difference between two sets $A$ and $B$.

If there are two sets $A$ and $B$, the set $\left(B-A\right)\cup \left(A-B\right)$ is the symmetric difference of two sets $A$ and $B$ and is denoted by $A∆B$.

$A∆B$ is represented by the shaded area of the Venn diagram.

Example: If $A=\left\{2,3,4,5,6,7,8\right\}$ and $B=\left\{1,3,5,6,7,8,9\right\}$ are two sets.

Then, $\left(B-A\right)\mathrm{and}\left(A-B\right)$ is given as follows:

$\begin{array}{rcl}A–B& =& \left\{2,4\right\}\\ B-A& =& \left\{1,9\right\}\end{array}$

$\begin{array}{rcl}& \Rightarrow & \left(B-A\right)\cup \left(A-B\right)=\left\{2,4\right\}\cup \left\{1,9\right\}\\ & \Rightarrow & A∆B=\left\{1,2,4,9\right\}\end{array}$

Hence, $A∆B=\left(B-A\right)\cup \left(A-B\right)$.