Learn exactly how to represent the union of sets using Venn diagram.The union set operations have the right to be visualized from the diagrammatic representationof sets.

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The rectangular an ar represents the universal collection U andthe circular areas the subsets A and B. The shaded part represents the setname listed below the diagram.

Let A and also B it is in the two sets. The union of A and also B is the setof every those aspects which belong either to A or come B or both A and also B.

Now we will usage the notation A U B (which is read as ‘Aunion B’) to denote the union of set A and set B.

Thus, A U B = x : x ∈ A or x ∈ B.

Clearly, x ∈ A UB   

⇒ x ∈ A or x ∈ B

Similarly, if x ∉ A U B  

⇒ x ∉ A or x ∉ B

Therefore, the shaded portion in the adjoining number represents A U B.


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Thus, us conclude indigenous the meaning of union of sets thatA ⊆A U B, B ⊆ A U B.

From the over Venn diagram the adhering to theorems are obvious:

(i) A ∪ A = A                        (Idempotent theorem)

(ii) A ⋃ U = U                       (Theorem of ⋃) U is the universal set.

(iii) If A ⊆ B, climate A ⋃ B = B

(iv) A ∪ B = B ∪ A                (Commutative theorem)

(v) A ∪ ϕ = A                      (Theorem of identification element, is the identification of ∪) 

(vi) A ⋃ A" = U                     (Theorem that ⋃) U is the universal set.

Notes:

A ∪ ϕ = ϕ ∪ A = A i.e. Union of any collection with the empty collection is always the set itself.

Solved examples of union the sets using Venn diagram:

1. If A = 2, 5, 7 and also B = 1, 2, 5, 8. Discover A U B making use of venn diagram.

Solution:

According to the given question us know, A = 2, 5, 7 and also B = 1, 2, 5, 8

Now let’s draw the venn diagram to uncover A union B.


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Solution:

According to the adjoining figure we get;

Set A = 0, 1, 3, 5, 8

Set B = 2, 5, 8, 9

Therefore, A union B is the set of elements which in collection Aor in collection B or in both.

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Thus, A U B = 0, 1, 2, 3, 5, 8, 9

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