2 Venn diagrams

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

Figure 1

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 $A=\left\{0,1\right\}$ and $B=\left\{0,1,2,3,4\right\}$ 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 $A\subseteq B$ . This is shown in the Venn diagram by $A$ being completely inside $B$ .

Figure 2 :

Task!

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

1. $A$ and $B$
2. $A^{\prime }$
3. $B^{\prime }$

Answer

Answer

Answer