﻿ Union, Intersection & Difference among sets Elementary Concepts of Set Theory

# Operations on sets

Like arithmetic operations, there are also operations on sets. They help us highlight the association among sets. The three basic operations are:

• union among sets
• intersection among sets
• difference among sets

Before discussing the operations, let us consider another form of depicting a set. In particular, depiction of association among sets. They are called Venn's diagram. Its application will be demonstrated along with discussion of the operation (below).

## Union among sets

Given three sets A, B and C, if any elements picked from either A or B are also elements of set C, then we say that C is the union of A and B. For example:

U : universe composes of family members

A : set of boys (children)

B : set of girls (children)

C : set of children

Then,

set of children, C is the union of A and B.

Mathematically, C = A ∪ B (Venn's diagram on the right)

Notice that the number of elements in C (4) is the sum of number of boys (2) and girls (2), i.e., 4 = 2 + 2. However, operation of union is not the same as arithmetic addition. This is demonstrated below. If,

D : set of females

E : set of mother and children

Then,

set of mother and children, E is the union of C and D.

Thus, E = C ∪ D

Observe that the number of elements in E, 5 ≠ 3 + 4.

## Intersection among sets

Given three sets A, B and C, if any elements picked from in-common elements of A and B are also elements of set C, then we say that C is the intersection of A and B. For example:

set of girls, B is the intersection of C and D.

Mathematically, B = C ∩ D.

## Difference among sets

Given three sets A, B and C, if any elements picked from A which is also not an element of B are elements of set C, then we say that C is the difference of B from A. For example:

set of boys, A is the difference of D from C

Mathematically, A = C - D.

Note that, set of mother = D - C.