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 :
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}
3. Symmetric difference of two sets
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