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Venn diagram is a way to visually represents relationship between groups of entities or objects. Venn diagrams are comprised of circles where each circle represents a whole set. Venn diagram can have unlimited circles but generally two or three circles are preferred otherwise the diagram becomes too complex.
Steps to draw a Venn Diagram
Consider the following sets of people:
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Cricket Players – $ C = { Ram, Shyam, Mohan, Rohan, Ramesh, Suresh } $
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Hockey Players – $ H = { Ramesh, Naresh, Mahesh, Leela, Sunita } $
Step 1: Draw a rectangle and label it as players.
Step 2: Draw two circles and label them as Cricket and Hockey. Make sure that circles are overlapping each other.
Step 3: Write Names inside the circle as relevant. Common name(s) should fall within common region.
Union
Union ($ cup $) represents a set where items are present in all categories but are not repeated.
Example
Problem Statement:
Draw a Venn diagram of $ C cup H $.
Solution:
Step 1: Determine players who are either playing cricket or hockey. Draw them as following:
$ C cup H = { Ram, Shyam, Mohan, Rohan, Ramesh, Suresh, Naresh, Mahesh, Leela, Sunita } $.
Intersection
Intersection ($ cap $) represents a set where items are present in both categories.
Example
Problem Statement:
Draw a Venn diagram of $ C cap H $.
Solution:
Step 1: Determine players who are playing cricket and hockey both. Draw them as following:
$ C cap H = { Ramesh } $.
Difference
Difference ($ – $) represents a set where items are present only in one category and not in other one.
Example
Problem Statement:
Draw a Venn diagram of $ C – H $.
Solution:
Step 1: Determine players who are playing cricket only. Draw them as following:
$ C – H = { Ram, Shyam, Mohan, Rohan, Suresh } $.
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