Topic 1: Set Theory

A set is a collection of objects such as numbers, points, shapes, ideas, etc.

The individual objects is a set are called the members or elements of the set.

There are 3 ways of writing down sets:

i) by description or by using the set builder notation.

ii) by listing its element  

  

   e.g. C = {a, b, c, d}

iii) by using a Venn diagram

Finite set

A finite set is a set which has finite number of members.

e.g. A = {2,4,6,8, ... 100}

Infinite set

An infinite set is a set which is not finite 

e.g [all triangles]

Universal set

A universal set is the set which contains all the available elements, denoted by E.

Empty set

The empty set or the null set is the set having no elements. It is denoted by [ ] or  ф

Note:  [ 0 ] and [ ф ] are not empty set as they have the element [ ] and ф respectively.

Subset

If every element of a set B is also a member of a set A, then we say B is a subset of A and write B ⊂ A. 

Intersection

The intersection of two sets A and B is the set of elements which is common to both A and B. it is denoted by A ∩ B and is read A intersect B. the shaded portion of the figure below shows A ∩ B.

Union

The union of two sets A and B is the set of elements which is in A or in B or in both A and B. it is denoted by A ∪ B and is read 'A union 'B. The shaded portion of the figure below shows A ∪ B.

Sets: Union and Intersection (Basic Video)