Learn how to represent the union of sets using Venn diagram. The union set operations can be visualized from the diagrammatic representation of sets.
The rectangular region represents the universal set U and the circular regions the subsets A and B. The shaded portion represents the set name below the diagram.
Let A and B be the two sets. The union of A and B is the set of all those elements which belong either to A or to B or both A and B.
Now we will use the notation A U B (which is read as ‘A union B’) to denote the union of set A and set B.
Thus, A U B = {x : x ∈ A or x ∈ B}.
Clearly, x ∈ A U B
⇒ x ∈ A or x ∈ B
Similarly, if x ∉ A U B
⇒ x ∉ A or x ∉ B
Therefore, the shaded portion in the adjoining figure represents A U B.
Union of Sets using Venn Diagram
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Thus, we conclude from the definition of union of sets that A ⊆ A U B, B ⊆ A U B.
From the above Venn diagram the following theorems are obvious:
Answers & Comments
Answer:
Union of Sets using Venn Diagram
Learn how to represent the union of sets using Venn diagram. The union set operations can be visualized from the diagrammatic representation of sets.
The rectangular region represents the universal set U and the circular regions the subsets A and B. The shaded portion represents the set name below the diagram.
Let A and B be the two sets. The union of A and B is the set of all those elements which belong either to A or to B or both A and B.
Now we will use the notation A U B (which is read as ‘A union B’) to denote the union of set A and set B.
Thus, A U B = {x : x ∈ A or x ∈ B}.
Clearly, x ∈ A U B
⇒ x ∈ A or x ∈ B
Similarly, if x ∉ A U B
⇒ x ∉ A or x ∉ B
Therefore, the shaded portion in the adjoining figure represents A U B.
Union of Sets using Venn Diagram
105Save
Thus, we conclude from the definition of union of sets that A ⊆ A U B, B ⊆ A U B.
From the above Venn diagram the following theorems are obvious: