DIFFERENCE OF TWO SETS

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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}

A Δ B = (A\B) u (B\A)

A Δ B = {1, 3} u {0, 7}

A 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

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