Symmetric difference is one of the important operations on sets.

Let us discuss this operation in detail.

Let X and Y be two sets.

Now, we can define the following new set.

**X Δ Y = (X \ Y) u (Y \ X)**

X Δ Y is read as "X symmetric difference Y"

Now that X Δ Y contains all elements in X u Y which are not in X n Y and the figure given below illustrates this. .

**Example : **

Let A = {1, 3, 5, 6}, B = {0, 5, 6, 7}, find A Δ B.

**Solution :**

A \ B = {1, 3, 5, 6} \ {0, 5, 6, 7} = {1, 3}

B \ A = {0, 5, 6, 7} \ {1, 3, 5, 6} = {0, 7}

A Δ B = (A \ B) u (B \ A)

A Δ B = {1, 3} u {0, 7}

A Δ B = {1, 3, 0, 7}

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