Using Venn Diagrams to Depict Relationships between Things

Here is an explanation of how to draw Venn diagrams for sets of things when they have different relationships with each other. Illustrative examples have been given for each and every case. I have explained disjoint sets, I have also explained the sets that intersect, and also the cases where one set is included inside another.

Last Reviewed and Updated on August 18, 2019
Posted by Parveen(Hoven),
Aptitude Trainer and Software Developer


Relationships between Sets of Things

Venn diagrams can be used to express relationships between real life things. The relationships between various things could be.

  1. Container Type(Physical):

    Parent child relationship, like India and Punjab have a parent child relationship. Punjab is owned or contained inside India. Another example is the relationship between House and Kitchen. I mean to say that one thing is physically contained inside another. More examples are Stable : Horse. Another example is Scabbard : Sword.

    Container Type(Physical) relatioship
  2. Container Type(Abstract):

    In this type of relationship the parent or owner is a conceptual thing. For example, every lion is an animal. We can say animal is the parent/container of lion. Another example is Planet and Jupiter. Here a planet is a conceptual parent of Jupiter. More examples are Stationery : Copy, Women : Mother, and so on. This hierarchy can be deepened to one like Continent : Country : India. Here Continent and Country are conceptual parent and grandparent of India.

    Container Type(Abstract) relationship
  3. Container Type(Measurement Units):

    Take for example, 10 decades make a century. So we can say that a Century is a container of Decade. On the same lines, a meter is a container of centimeter, which in turn is a container of millimeter. Similarly, Hundreds are a parent of Tens, and Tens, in turn are a parent of Units.

    Container Type(Measurement Units
  4. Common Area:

    Two sets of things share a common area. For example, some doctors are men, or vice versa, some men are doctors. Two sets are involved here. One set is the set of doctors, and the other is the set of men. They are not related as parent-child because all men are not doctors, and neither all doctors are men. But some doctors are men, and some men are doctors. When the word "some" comes, it signifies a common area.

  5. No Relation:

    Two things may be totally un-related, for example, vegetarians and non-vegetarians have nothing in common. Neither do they have the parent child relation.

    No Relation

    Another example is the relation between dog, cow and horse. They are three different physical things that are entirely different. You should ask questions like this: are any dogs cows?

    No Relation between three disjoint sets
  6. Two Sets Inside Another:

    We can use Venn diagrams to represent relationships between three things, out of which two are children of the third. For example, brother and son are both of the male type. So they can be put inside the set for male, who is their parent. Again, brother and son can share a common relation because a son can be a brother of another person.

    Two Sets Inside Another
  7. Three Sets with One Single Common Portion:

    Just like two sets can have one common area, sets of 3 things can have a common area as well. For example the set of doctors, teachers and models can have a single common area. Some doctors can be teachers, and they can be models too. Please note that no two of these items have a parent child relation. They are three independent sets having some area in common with them.

    Three Sets with One Single Common Portion
  8. Three Sets out of Which Only Two Pairs have a Common Area:

    Instead of three sets having one common area, it is also possible that only two pairs share a common area, but the third pair is not related at all. For example, models, men and women are three such sets. Some men are models, some women are models, but no men are women.

    Three Sets with One Single Common Portion
  9. Three Sets Out of Which Two are Parent-Child but Third is Not Related To Either:

    This is another common relation. Consider these three sets: Criminals, Robbers and Judges. We can see that all robbers are criminals, so the two sets have a parent child relationship. Whereas, no judge is a criminal.

    Three Sets Out of Which Two are Parent-Child but Third is Not Related To Either
  10. Three Sets out of Which Two are Parent-Child and Third Shares a Commonality with Both:

    This one seems to be very complicated, but if you ask the right questions, then it is easier to crack. Consider the three sets: Doctors, Surgeons and Models. How is a doctor related to a surgeon? All surgeons are doctors, so the relation is parent-child. How is a model related to them? Some models are doctors, and some models are surgeons. The relationships are common type. So we should have a circle inside a circle, and a third circle crossing both of them.

    Three Sets out of Which Two are Parent-Child and Third Shares a Commonality with Both

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This Blog Post/Article "Using Venn Diagrams to Depict Relationships between Things" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2019-08-18.