AVenn diagramis a diagram that shows all possiblelogical relations between a finite collection of different sets

**Introduction**

Venn charts, named after the English mathematician** John Venn**, which introduced their use in** 1881**, Venn diagram can be used to represent **sets** graphically. In Venn diagrams the **universal set **U which contains all the subjects that are shown as a rectangle.

In this rectangle, the circles or other **geometric figures** are used to represent the sets.( Note that the universal sets vary depending on which **objects** are of interest.) Sometimes points represent the specific elements of the set

These** diagram**s shows elements as **points in the plane**, and sets as regions inside closed curves. A Venn diagram consists of multiple **overlapping** closed curves, usually circles, each representing a set. The points inside a **curve** represent elements of the set *S*, while points outside the** boundary** represent elements not in the set *S*.[wikipedia]

Venn diagrams can be used to** illustrate** that a set A is a subset of a set B. We draw the** universal set** S as a rectangle.Within this rectangle we draw a circle for B and a circle for A .

## Union

Let A and B be subsets of a universal set U. The union of sets A and B is the set of all elements in U that belong to A or to B or to both, and is denoted A ∪ B.

Symbolically:

A ∪ B = {x ∈U | x ∈A or x ∈ B

**EXAMPLES:**

**(1) **If *A* = {1, 3, 5, 7} and *B* = {1, 2, 4, 6} then *A* ∪ *B* = {1, 2, 3, 4, 5, 6, 7}.

**(2)**

*A* = {*x* is an even integer larger than 1}

*B* = {*x* is an odd integer larger than 1}

[latex]{\displaystyle A\cup B=\{2,3,4,5,6,\dots \}}[/latex]

**(3)** Let U = {1, 2, 3, 4, 5, 6, 7}

A = {1, 3, 5, 7}, B = {2, 4, 5, 6}

Then A ∪ B = {x ∈U | x ∈A or x ∈ B}

={1, 3, 4, 5 ,6, 7}

**VENN DIAGRAM FOR UNION:**

**MEMBERSHIP TABLE FOR UNION:**

## INTERSECTION:

Let A and B subsets of a universal set U. The intersection of sets A and B is the set of all elements in U that belong to both A and B and is denoted as A ∩ B.Symbolically:

A ∩ B = {x ∈U | x ∈ A and x ∈B}

Intersection is an associative operation; that is, for any sets *A*, *B*, and *C*, one has *A* ∩ (*B* ∩ *C*) = (*A* ∩ *B*) ∩ *C*. Intersection is also commutative; for any *A* and *B*, one has *A* ∩ *B* = *B* ∩ *A.* It thus makes sense to talk about intersections of multiple sets. The intersection of *A*, *B*, *C*, and *D*, for example, is unambiguously written *A* ∩ *B* ∩ *C* ∩ *D*. [Wikipedia]

**VENN DIAGRAM FOR INTERSECTION:**

**MEMBERSHIP TABLE FOR INTERSECTION:**

**DIFFERENCE:**

Let A and B be subsets of a universal set U. The difference of “A and B” (or relative complement of B in A) is the set of all elements in U that belong to A but not to B, and is denoted A – B or A \ B.

Symbolically:

A – B = {x ∈U | x ∈ A and x ∈B}

**EXAMPLE:**

Let U = {a, b, c, d, e, f, g}

A = {a, c, e, g}, B = {d, e, f, g}

Then A – B = {a, c}

**VENN DIAGRAM FOR SET DIFFERENCE:**

**MEMBERSHIP TABLE FOR SET DIFFERENCE:**

## COMPLEMENT:

Let A be a subset of universal set U. The complement of A is the set of all element in U that do not belong to A, and is denoted AN, A or Ac

Symbolically:

A^{c}= {x ∈ U | x ∉ A}

**EXAMPLE:**

Let U = {a, b, c, d, e, f, g]

A = {a, c, e, g}

Then A^{c} = {b, d, f}

**VENN DIAGRAM FOR COMPLEMENT:**

**MEMBERSHIP TABLE FOR COMPLEMENT:**