# SYMMETRIC DIFFERENCE OF TWO SETS

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}

Δ B  =  (A \ B) u (B \ A)

Δ B  =  {1, 3} u {0, 7}

Δ B  =  {1, 3, 0, 7}

## Related Pages

1. Union of sets

2. Intersection of sets

3. Set difference

4. Complement of a set

5. Disjoint sets Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here. Kindly mail your feedback to v4formath@gmail.com

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