Venn Diagrams Explanations

Venn Diagrams

Venn diagrams are part of the assessment that many people struggle with. You have to teach yourself to look at each question in the same way and not to rely too much on your feelings. Many assignments are designed to mislead you, so if you only rely on your feelings, you will make mistakes. Below is an example where you cannot rely on your feelings.

Which figure best represents the relationship between the following three collections?

  1. Pancakes
  2. Syrup
  3. Syrup Bottles


image2.png



You might think, you can put syrup in a syrup bottle and use the syrup bottle to put the syrup on your pancake. However, this does not lead you to the correct answer. The question is always whether there is an overlap between the collections.

Therefore always ask yourself:

All these questions are answered with “never” in this case, so the correct answer must be A. The collections are completely separate from each other.

Start practicing venn diagrams

In the exercises you receive on your assessment, there are 11 possible ways to represent the relation between 3 collections. Below we give an example for each possibility.

  1. The three collections are completely separate from each other.

venn-diagrams2.png

An example of three collections that can best be represented as this:

  1. Vacationers
  2. Airplanes
  3. Plane tickets

There is no possible overlap between the collections, so they should not overlap in the figure.

  1. A collection completely separate, another collection completely within another collection.
venn-diagrams3.png

An example of three collections that can best be represented as follows:

  1. Taxis
  2. Means of transport
  3. Taxi drivers

A taxi is always a means of transport and a means of transport is sometimes a taxi. This is therefore represented by a smaller circle (the taxis) in a larger circle (the means of transport).

The taxi drivers do not overlap with the other collections, so they should be shown separately.

  1. Two collections overlap and a third collection falls entirely within the other two collections.
venn-diagrams4.png

An example of three collections that can best be represented like this:

  1. Birds
  2. Black animals
  3. Adult crows

So you can see that the collection of crows must fall completely within the other collections and that the collection of birds and black animals overlap with each other, but also have parts where they don’t overlap.

4) Two collections partly overlap and completely fall within a third collection.

venn-diagrams5.png

An example of three collections that can best be represented like this:

  1. Sweet dogs
  2. Labradors
  3. Animals

You see that labradors and sweet dogs partly overlap and partly do not. But naughty labradors, sweet labradors (the part that overlaps with sweet dogs) and all other sweet dogs are completely within the collection of animals.

5) A collection falls entirely within another collection, which falls entirely within another collection.

venn-diagrams6.png

An example of three collections that can best be displayed like this:

  1. Dogs
  2. Labradors
  3. Animals

You can see that the collection of labradors is completely within the collection of dogs and that the collection of dogs is completely within the collection of animals.

6) Two collections are completely separate, but both fall within a third collection.

venn-diagrams7.png

  1. Dogs
  2. Cats
  3. Animals

You can see that the collection of cats is completely separate from the collection of dogs, but that both collections are completely within the collection of animals.

7) A collection overlaps with two other collections, which in turn are completely separate

venn-diagrams8.png

  1. Dogs
  2. Cats
  3. Sweet animals

You can see that the collection of cats is completely separate from the collection of dogs, but that both collections overlap with the collection of sweet animals. However, they don't fall in the collection completely, because there are also naughty cats and dogs.

8) A collection falls entirely within a second collection. A third collection overlaps with the second collection and is completely separate from the first collection

venn-diagrams9.png
  1. Sweet dogs
  2. Cats
  3. Sweet animals

You can see that the collection of cats is completely separate from the collection of sweet dogs, but overlaps with the collection of sweet animals. The collection of sweet dogs falls entirely within the collection of sweet animals.

9) Three collections all overlap

venn-diagrams10.png
  1. Sweet dogs
  2. Puppies
  3. Labradors

You can see that the collections can all be each other, but also cannot be each other. The piece where they all overlap are the sweet labrador puppies :)

10) Two collections overlap with each other and are completely separate from a third collection

venn-diagrams11.png
  1. Sweet dogs
  2. Puppies
  3. Cats

You can see that the collections of puppies and sweet dogs overlap with each other, but they cannot be each other. Both collections are completely separate from the collection of cats.

11) Two collections overlap with each other and a third collection falls entirely within one of the collections and partly in the other collection

venn-diagrams12.png

  1. Sweet dogs
  2. Labradors
  3. Labrador puppies

You can see that the collection of labrador puppies falls entirely within the collection of labradors and partly overlaps with the collection of sweet dogs (think of the naughty labrador puppies). The collection of labradors has an overlap with the collection of sweet dogs. (think naughty labradors and sweet dachshunds on the other hand).


Venn Diagrams practice sets