Venn diagram: A Venn diagram (also known as a set diagram or
logic diagram) is a diagram that shows all possible logical relations between a
finite collection of different sets.
It represents the mathematical or logical sets
pictorially as circles or closed curves within an enclosing rectangle, common elements of the sets
being represented by intersections of the circles.
Set: A set is a group or collection of
objects or numbers, considered as an entity unto itself. Each object or number
in a set is called a member or element of the set.
Example 01: 26 English alphabet from a
set and if we consider two objects ‘x’
and ‘α’ then x is an element in the set but α
is not an element in the set.
Example 02: Sets of numbers:
Set of whole
numbers: {0, 1, 2, 3, ...}
Set of prime
numbers: {2, 3, 5, 7, 11, 13, 17, ...}
Representation of Venn diagram
Take the three sets:
A = {1, 2, 5}
B = {1, 6}
C = {4, 7}
The Venn diagram of these sets is:
This chapter
deals with the logical problems with diagrams. The knowledge of a set and its
diagrammed representation is sufficient for this chapter. Here is some standard
representations given bellow.
1. Three
different groups or sets; ‘A’, ‘B’ and ‘C’.
2. If two
sets ‘A’ and ‘B’ are partly related and third is different.
3. If ‘A’ is partly related to ‘B’ and ‘B’ is partly related to ‘C’.
4. If ‘A’, ‘B’
and ‘C’ are partly related to each other.
5. If ‘A’
belongs to set ‘B’ and ‘B’ belongs to set ‘C’.
6. If two
different sets ‘A’ and ‘B’ belongs to Set ‘C’.
7. If two
partly related sets ‘A’ and ‘B’ belongs to set ‘C’.
8. If ‘A’ belongs to ‘B’ and both of them is partly related to ‘C’.
Example: Question No 01 & 02
Choose the most suitable diagram for given
items. The diagrams are;
Question No. 01: Boy, Student,
Cricketer
Answer: Option B
Question No. 02: Cancer, Aids,
Disease
Answer: Option E
Venn Diagram:
Formula: Venn Diagram Formulas
Solved Examples: Solved Examples: Set 01
Practice Test: Practice Test: 01 Practice Test: 02
Formula: Venn Diagram Formulas
Solved Examples: Solved Examples: Set 01
Practice Test: Practice Test: 01 Practice Test: 02