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**Set Theory Concepts**

∙ Introduction

∙ Definitions

∙ Universe & Subsets

∙ More on subsets

∙ Operations on sets

∙ Properties of operations

∙ Set graphs & Line graphs

∙ Introduction

∙ Definitions

∙ Universe & Subsets

∙ More on subsets

∙ Operations on sets

∙ Properties of operations

∙ Set graphs & Line graphs

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).

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.

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.

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.