1.4 Cardinality & Counting Principles

By the end of this lesson, you will be able to apply the counting principle in Set Theory

Lesson 1 of 5: Cardinality

The dictionary defines a Cardinal as a leading dignitary of the Roman Catholic Church. Cardinals are nominated by the Pope, and form the Sacred College which elects succeeding popes.

However, in mathematics, Cardinality has a totally different meaning from Cardinal. Let's watch the video below.

https://www.youtube.com/watch?v=SY0ixs-_IGc

What is the Cardinality of a Set? | Set Theory, Empty Set

Lesson 2 of 5: What have I learnt?

Let's summarize what you have learnt from the video.

Cardinality

The number of elements in a set A is called the Cardinality or size of A, denoted by |A|. For example, if  A = {1,3,5,7}, then |A| = 4.

Lesson 3 of 5: Difference and Addition of Sets

Difference of Two sets : A –B  (Subtraction)

The difference of two sets A and B,i.e.  A-B,  is the set of elements belonging to A and not B.

In the example on the left,

• A- B is the sets of elements belonging to A and not B.
• B-A is the sets of elements belonging to B and not A.

Addition of 2 Sets : A + B

In Figure 1, where A and B are disjoint sets,

A+B =A∪B

n(A+B) =n(A∪ B)

In Figure 2, where A and B are notdisjoint sets,

n(A∪B)=n(A)+ n(B)- n(A∩B)

This is because adding sets A and B will add the common elements twice. Let's look as some examples next.