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

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