Venn Diagram Analytical Reasoning Formulas - ObjectiveBooks

Venn Diagram Analytical Reasoning Formulas

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:
Representation of  Venn diagram

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’.
Venn diagram formula 01

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.
Venn diagram formula 04

5. If ‘A’ belongs to set ‘B’ and ‘B’ belongs to set ‘C’.
Venn diagram formula 05

6. If two different sets ‘A’ and ‘B’ belongs to Set ‘C’.
Venn diagram formula 06

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’.
Venn diagram formula 08

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
Venn diagram Example 01

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

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