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
3. Symmetric difference of two sets
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