SETS

The set is a well-defined group of objects called elements that have something in common or follow a certain rule. Set notation uses braces { } with elements separated by commas. The braces indicate that the objects written between them belong to the set.

       The number of elements is called CARDINALITY. Therefore the cardinality of the set is 3.

Activity 1

Can you group, name and list the following objects?

1. How many sets are there? ANSWER

2. Can you name each set? ANSWER

3. Name the elements of each group. ANSWER

Learning Task 1:

Identify all the possible answers for the statements below.

1. Colors of the rainbow

  Set C = { red, orange, yellow, green, blue, indigo, violet }

2. Letters used in the word "Mathematics"

  Set M = { m,a,t,h,e,i,c,s }

3. Grade 7 sections of Santiago NHS

  Set S = { Aquino, Bonifacio, Jacinto, Laurel, Ponce }

UNION AND INTERSECTION

Union of sets. The union of two sets is the set of all elements that belong to both A or B. It is denoted by AUB and is read as “union of A and B”

Intersection of Sets. The intersection of two sets is the set of all elements that are common to both sets. It is denoted by A∩B and is read as “A intersection B”

Activity 1

1. Describe Set A
2. Describe Set B
3. What is AUB?
4. What is A∩B?

ANSWER

Activity 2

Can you identify the elements in each set?

1. What are the elements of A? 

2. What are the elements of B?

3. What are the elements of A only? 

4. What are the elements of B only? 

5. What is the union of A and B? 

6. What is the intersection of A and B? 

ANSWER

COMPLEMENT OF A SET

The complement of a set A', is the set of all elements found in the universal set U, that are not found in set A.

The universal set U is the set that contains all objects under consideration.

From the given example, the universal set is

U = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }

The complement of set A is

A' = { 4, 7, 6, 3 }

From the universal set, we can also get subsets. 

Subsets are elements of A that are also elements of the universal set U.

   

Example

U = { 1, 2, 3, 4 }

The subsets are:

{ 1 } { 2 } { 3 } { 4 }

{ 1, 2 } { 1, 3 } { 1, 4 } { 2, 3 } { 2, 4 } { 3, 4 }

{ 1, 2, 3 } { 1, 2, 4 } { 2, 3, 4 } { 1, 3, 4 }

{ 1, 2, 3, 4 } {  }

Therefore, there are 16 subsets. 

 {  }  This is called a NULL set. Null set is an empty set. It is a subset of all set.