DIFFERENCE OF TWO SETS

Set difference is one of the important operations on sets which can be used to find the difference between two sets.

Let us discuss this operation in detail.

Let X and Y be two sets.

Now, we can define the following new set.

X\Y = {z | z ∈ X but z ∉  Y}

(That is z must be in  X and must not be in Y)

X\Y is read as "X difference Y"

Now that X\Y contains only elements of X which are not in Y and the figure given below illustrates this.

Some authors use A - B for A\B. We shall use the notation A\B which is widely used in mathematics for set difference. 

Example 1 :

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

Solution :

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

A\B = {1, 3}

Example 2 :

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

Solution :

A Δ B = (A\B) u (B\A)

A\B = A - B

= {1, 3, 5, 6} - {0, 5, 6, 7}

= {1, 3}

B\A = 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}

Note :

A\B is read as "A difference B"

A Δ B is read as "A symmetric difference B"

A\B ≠ A Δ B

Related Pages

1. Union of sets

2. Intersection of sets

3. Symmetric difference of two sets

4. Complement of a set

5. Disjoint sets

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