SETS

SETS

- Any collection of well-defined objects.

TYPES OF SETS

1. Roster method or list method

- this is the representation by listing down the elements of the set.

- a set that has an element listed and is separated by a comma.

ILLUSTRATION:

Set A = { a,e,i,o,u}

Set B = { 1,2,3,4,5,6 }

Set C = { 1,2,3,4….}

Set D = { nurse, doctor,patient}

2. Rule Method

- a set where the members are described.

- this is a set that is representing its element by a statement.

ILLUSTRATION:

Set A = { x/x is a set of vowel in an English Alphabet}  [this means Set A = { a,e,i,o,u}]

Set B = { x/x is a counting numbers less than 7}  [this means Set B = { 1,2,3,4,5,6}]

Set C = { x/x is a set of counting numbers}  [this means Set C = { 1,2,3…..}]

Exercises:

Let U = { x / x is a counting number less than 10}

      

       A₁ = {1, 2, 4, 6, 8}

       A₂ = {2, 4, 5, 9}

       A₃ = {x/x is a positive integer and x² ≤ 16}

       A₄ = {7, 8}

      Compute:

1.            A₁  U  A₂

2.            A₁  U  A₂  U  A₃  

3.            A₁  ∩   A₂  ∩  A₃  

4.            A₁ ∩  (A₂  U  A₃)  

5.            (A₁ U A₂)’  

6.         A₁  U  (A₂   ∩  A₃)  

7.         A'₃ U  A₁ 

_8.           A₂  ∩  A₃  

_9.           A­­₄ ∩ (A₂  U  A₃)'

10.        (A­­₄ U A₁)  ∩  (A₂  U  A₃)