Venn Diagram: Definition
A Venn diagram can be defined as an illustration of the relationships between and among sets and/or groups of objects that share something in common. Usually, Venn diagrams are used to depict set intersections as given below.
The drawing is an example of a Venn diagram that shows the relationship among three overlapping sets X, Y, and Z.
There are some regions which are common to X & Y(X ∩Y), X & Z (X ∩Z),Y & Z (Y ∩Z) and all three of X,Y,Z (X ∩Y ∩Z). These are called intersecting regions.
A typical three-set Venn diagram can be represented as follows:
Some important Venn Diagrams:
All A are B
This implies that A is a subset of B i.e. A is encompassed in B but not necessarily vice versa.
A = B
This implies that both A and B are subsets of each other A i.e. both the A and B are contained in each other.
No A are B
This implies that both A and B are not contained in each other i.e. it can be said that both A and B are independent sets.
Some A are B
Here some part of A and some part of B are intersecting and also, some B areA also holds true.
Some A are not B
Here, this implies that some part of A is surely not included in B and it is uncertain whether the remaining part of A is included in B or not.
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