What is Venn Diagram? || Why Venn diagram is so important? || Operations on Venn Diagrams of sets

What is Venn Diagram and why the Venn diagram is so essential?

• The graphical representation of the sets and their operations using geometrical shapes is called the Venn diagram.
• The English mathematician John Venn introduced Venn Diagram in $1881 AD$.
• The universal set $∪$ is usually represented by a rectangle.
• Inside the rectangle circle or oval represents sets.

Example:
If $A$ $=\{1, 2, 3\}$   and  $B$ $=\{3, 4, 5\}$,  $U$ $=\{1, 2, 3, 4, 5\}$
then their Venn diagram is

Solution:

Operations on sets and Venn Diagram

1.    Union of two sets

$A\cup B$ $=\{x:x\epsilon A$ or $\epsilon B\}$

Example:
$A$ $=\{1, 2, 3\}$,  $B$ $=\{2, 3, 4\}$  then  $A\cup B$ $=\{1, 2, 3, 4\}$

2.    The intersection of two sets

$A\cap B$ $=\{x:x\epsilon A$  $\wedge$  $x\epsilon B\}$

$A\cap B$ $=\{3, 4\}$

3.    Difference between two sets

$A-B$ $=\{x:x\varepsilon A$ and $x\notin B\}$.

It is also written as $A\cap B'$
Similarly  $B-A$ $=B\cap A'$

E.g.
$A$ $=\{1, 2, 3\}$,  $B$ $=\{2, 3, 4\}$

$A-B$ $=\{1\}$  and  $B-A$  $=\{4\}$

$A-B$ $=\{1\}$

$B-A$ $=\{4\}$