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.
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.
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.
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.
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
● Set Theory
● Sets Theory
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● Problems top top Union that Sets
● Problems top top Intersection the Sets
● Difference of two Sets
● Complement the a Set
● Problems on enhance of a Set
● Problems on operation on Sets
● Word problems on Sets
● Venn Diagrams in DifferentSituations
● Relationship in Sets utilizing VennDiagram
● Union of Sets making use of Venn Diagram
● Intersection that Sets using VennDiagram
● Disjoint of Sets making use of VennDiagram
● Difference the Sets using VennDiagram
● Examples top top Venn Diagram
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