UNION OF SETS

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Union is one of the important operations on sets which can be used to combine two or more sets to form another set.

Let us discuss this operation in detail.

Let X and Y be two sets.

Now, we can define the following new set.

X u Y = {z | z ∈ X or z ∈ Y}

(That is, z may be in X or in Y or in both X and Y)

X u Y is read as "X union Y"

Now that X u Y contains all the elements of X and all the elements of Y and the figure given below illustrates this.

It is clear that X ⊆ X u Y and also Y ⊆ X u Y

Example 1 :

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

Solution :

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

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

Example 2 :

Let A = {-1, 0, 2, 3, 4}, B = {0, 3, 4, 5} and C = {0, 4, 5, 7}. Find (A n B) u (B n C).

Solution :

A n B = {-1, 0, 2, 3, 4} n {0, 3, 4, 5}

A n B = {0, 3, 4}

B n C = {0, 3, 4, 5} n {0, 4, 5, 7}

B n C = {4, 5}

(A n B) u (B n C) = {0, 3, 4} u {4, 5}

= {0, 3, 4, 5}

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