2 Venn diagrams

Sets are often represented pictorially by Venn diagrams (see Figure 1).

Figure 1

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Here A , B , C , D represent sets. The sets A , B have no items in common so are drawn as non-intersecting regions whilst the sets C , D have some items in common so are drawn overlapping.

In a Venn diagram the universal set is represented by a rectangle and sets of interest by area regions within this rectangle.

Example 3

Represent the sets A = { 0 , 1 } and B = { 0 , 1 , 2 , 3 , 4 } using a Venn diagram.

Solution

The elements 0 and 1 are in set A , represented by the small circle in the diagram. The large circle represents set B and so contains the elements 0,1,2,3 and 4. A suitable universal set in this case is the set of all integers. The universal set is shown by the rectangle.

Note that A B . This is shown in the Venn diagram by A being completely inside B .

Figure 2 :

{The set A is contained completely within B}

Task!

Given A = { 0 , 1 } and B = { 2 , 3 , 4 } draw Venn diagrams showing  

  1. A and B
  2. A
  3. B

Note that A and B have no elements in common. This is represented pictorially in the Venn diagram by circles which are totally separate from each other as shown in the diagram.

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The complement of A is the set whose elements do not belong to A . The set A is shown shaded in the diagram.

{The complement of A contains elements which are not in A.}

The set B is shown shaded in the diagram.

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