Venn Diagrams: Definition, Rules, Sample Questions, Tips and FAQs

Venn diagrams are essentially a pictorial representation of sets using circles. They are used to represent individual sets and depict operations between sets and showcase relations between two or more sets. They were first introduced by John Venn in the 19th Century, and are also called set diagrams or logic diagrams. Venn Diagram is used for Set operations such as union and intersection, as well as arithmetic operations such as addition and subtraction.

Set Operations Using Venn Diagrams

Ref: NCERT

Questions based on Venn Diagram are often asked in MBA entrance exams too. Candidates preparing for CAT, XAT, MAT, CMAT, IIFT, SNAP and other MBA entrance exams must study Venn Diagram as a topic and its variations. 

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Venn diagrams can also be used to show subsets and complements of sets. In a Venn diagram, it isn’t just the circles that depict the sets that are important. The box that encloses these circles is also a part of the Venn diagram and is equally important. This is because the region interior to this box represents the universal set.

Using the Venn diagram, you cannot just depict the complements of individual sets, but also the complements of unions and intersections of two or more sets. These are difficult to express using set equations, but Venn Diagrams make them easier.

Also Read: MBA Preparation 2024: Tips to Prepare for MBA Entrance Exams

Illustrated Examples:

• Set A is the set of all non-negative real numbers. Set B is the set of whole numbers. What is the intersection of A and B?
  The intersection of A and B is the number 0.
  

• If Set A has 10 elements, Set B has 4 elements, and both the sets have 2 elements in common, how many elements does the union of A and B have?
  The union of A and B has n(A) + n(B) - n(AB) elements
  = 10 + 4 - 2
  = 12
  
• What is the complement of the set of rational numbers, if the universal set is the set of real numbers?
  The complement of the set of rational numbers is the set of irrational numbers.

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