Venn Diagrams for the Assam Police Constable (AB & UB) Exam
Venn Diagrams is a reasoning topic of the SLPRB Assam Police Constable (AB & UB) examination in which sets of things are shown by circles and the candidate must choose the diagram that correctly shows the relation between them, or must find a number from a given diagram. The questions need no general knowledge about the items beyond the ordinary relation between them, such as whether one group is a part of another or is entirely separate. The whole topic is visual, and a candidate who practises the common relations answers quickly. This page explains the types of relations, the method of choosing a diagram, the region counting formula and the traps that cost marks. The material follows the standard reasoning reference books used for Assam recruitment examinations and is reviewed before it is published.
What the Topic Means
A Venn diagram shows sets by circles. When two sets have some members in common, their circles overlap. When one set is fully contained in another, one circle lies inside the other. When the two sets have nothing in common, the circles are drawn separately. In the examination the candidate is given three or four classes, such as fruits, mangoes and living things, and must choose the figure that shows their relation, or is given the figure and asked to find the number of members in a region.
The Three Relations Between Two Sets
- Disjoint sets: two classes with nothing in common, shown by two separate circles, such as chairs and apples.
- Intersecting sets: two classes with some members in common, shown by two overlapping circles, such as teachers and men.
- Contained sets: one class is completely inside another, shown by one circle inside another, such as mangoes inside fruits.
Choosing the Right Diagram
- Ask whether one class is a part of another, and if so, draw the smaller circle inside the larger one.
- Ask whether the two classes share some members, and if so, draw the circles overlapping.
- Ask whether the classes are entirely separate, and if so, draw the circles apart from each other.
- For three classes, sort them by this relation and place the circles accordingly.
- Check the chosen figure with one example, such as a mango for the class of fruits.
Region Counting and Inclusion-Exclusion
When a diagram is given with numbers, the candidate must find the number in a region or the total. If members belong to both of two groups, they are counted twice, so the rule is that the number in either group equals the number in the first plus the number in the second minus the number in both. For example, if 20 like tea, 15 like coffee and 5 like both, the number who like at least one is 20 plus 15 minus 5, that is 30. The number who like only tea is 20 minus 5, that is 15, and the number who like only coffee is 15 minus 5, that is 10.
Worked Examples
Example one: for the classes Fruits, Mangoes and Flowers, the mango circle lies inside the fruit circle, and the flower circle is separate, so the correct figure has a small circle inside a large circle and a third circle apart from both. Example two: for the classes Men, Fathers and Doctors, all fathers are men, so the father circle is inside the man circle, while doctors may be men or women, so the doctor circle overlaps the circle of men. Example three: if 30 students play cricket and 20 play football with 10 playing both, then 40 students play at least one game, since 30 plus 20 minus 10 is 40.
How This Topic Appears in the Examination
The topic usually appears as two to four objective questions of one mark each. The common forms are to choose the diagram that best represents a given group of classes, to find the number of members in a particular region of a given diagram, and to find the total or the number belonging to both groups. The figures are small and the questions are quick.
Shortcuts and Speed Methods
- Test each class with one concrete example before choosing the figure.
- Remember that a special class lies inside a general class, such as mangoes inside fruits.
- Use the inclusion-exclusion formula, n(A or B) equals n(A) plus n(B) minus n(A and B).
- Read the region of the diagram carefully, since only and both mean different regions.
- For three groups, fill the innermost region first, then the two-group regions, then the single regions.
Common Mistakes to Avoid
- Forgetting that a member in both groups is counted twice and must be subtracted once.
- Confusing the class that is a part with the class that is a whole.
- Drawing overlapping circles for two classes that cannot share a member.
- Reading only when the question asks for both, or the reverse.
- Not testing the diagram with a concrete example.
Preparation Plan
- Learn the three relations between two sets.
- Practise choosing diagrams for twenty sets of classes a day.
- Learn the inclusion-exclusion formula and use it in region questions.
- Practise filling the regions of a three-circle diagram from the inside out.
- Revise the common classes once a week.
More Practice Questions
- For the classes Doctors, Human beings and Women, the doctor circle and the woman circle both lie inside the circle of human beings and overlap each other.
- If 40 like tea, 30 like coffee and 10 like both, then 60 like at least one.
- For the classes Squares, Rectangles and Circles, the square circle lies inside the rectangle circle and the circle is separate.
- If 50 students take English, 40 take Hindi and 15 take both, the number who take only English is 35.
- For the classes Teachers, Musicians and Men, all three circles overlap in some way.
Quick Revision Checklist
- Disjoint, intersecting and contained sets.
- Part inside whole, and special inside general.
- Inclusion-exclusion for the either-or count.
- Only and both mean different regions.
- Always test with a concrete example.
Frequently Asked Questions
What is a Venn diagram?
A Venn diagram is a figure in which sets of things are shown by circles, so that overlapping circles mean common members, a circle inside another means one set is a part of the other, and separate circles mean no common members.
How do I choose the right diagram in the exam?
Test each class with a concrete example and ask whether one class is part of another, whether the two share some members, or whether they are entirely separate, and then place the circles accordingly.
What is the inclusion-exclusion formula?
The number in either of two groups equals the number in the first plus the number in the second minus the number in both, because the members of both are counted twice and must be subtracted once.
What is the difference between only and both in a region question?
The members who are in both groups lie in the overlap of the two circles, while the members who are in only one group lie in the part of that circle which does not overlap the other.
Is Venn diagram scoring in Assam Police?
Yes. The figures are small, the relations are few, and the region questions use one simple formula, so it is a good topic for sure marks.