# Symmetric Difference of Two Sets – Venn Diagram and Examples

Here you will learn what is the symmetric difference of two sets with venn diagram and examples.

Let’s begin –

## Symmetric Difference of Two Sets

Definition : Let A and B be two sets. The symmetric difference of sets A and B is the set (A – B) $$\cup$$ (B – A) and is denoted by $$A \Delta B$$.

Thus, $$A \Delta B$$ = (A – B) $$\cup$$ (B – A) = {x : x $$\in$$ A $$\cap$$ B}

Also Read : Formulas and Operation of Sets

## Venn Diagram : The grey coloured region in the above figure represents $$A \Delta B$$.

Example : If A = {1, 2, 3, 4, 5, 6, 7, 8}  and B = {1, 3, 5, 6, 7, 8, 9}. then find $$A \Delta B$$.

Solution : We have sets A and B,

A – B = {2, 4} and B – A = {9}

$$\therefore$$ $$A \Delta B$$ = (A – B) $$\cup$$ (B – A) = {2, 4, 9}

Example : If A = {x $$\in$$ R : 0 < x < 3}  and B = {x $$\in$$ R : 1 $$\le$$ x $$\le$$ 5}. then find $$A \Delta B$$.

Solution : We have sets A and B,

A – B = {x $$\in$$ R : 0 < x < 1}

B – A = {x $$\in$$ R : 3 $$\le$$ x $$\le$$ 5}

$$\therefore$$ $$A \Delta B$$ = (A – B) $$\cup$$ (B – A) = {x $$\in$$ R : 0 < x < 1} $$\cup$$ {x $$\in$$ R : 3 $$\le$$ x $$\le$$ 5}

$$\implies$$  $$A \Delta B$$ = {x $$\in$$ R : 0 < x < 1 or 3 $$\le$$ x $$\le$$ 5}