SETS

Introduction

     Forget everything you know about "numbers". Instead of math with numbers, we will now think about "math with THINGS".

     Sets are the fundamental property of mathematics. Sets, by themselves, seem pretty pointless. But it's only when we apply sets in different situations that they become the powerful building blocks of mathematics.

     Think of this. If you watch a volleyball match, you will often hear something like "Philippines is now up a SET". On this note, what is the meaning of SET??? 

 

        But in mathematical sense, "What is a SET?" 

Task

          At the end of the discussion, students are expected to:

  1. Define sets.

  2. Differentiate appropriately set notations.

  3. Enumerate sets found in our surroundings. 

Process

          Students will have a short individual seatwork.

  -Seatwork-

   *Using a one whole sheet of pad paper, answer the following:

 I. Define "SETS" in your own words.

 II. What do these notations represents?

           { }                       -

           =                        -

       A, B, C, ... Z          -

           n                        -

           U                       -

         <—>                     -

           €                        -

 III. Write down "sets" found in your surroundings as many as you can. 

   

Evaluation

 ---Scoring table---

Tests Scores
Test I.      3
Test II.      7
Test III.     10

       Total -   20pts

 

Note:

For Test I. ,

               3pts - excellent

               2pts - satisfactory

                1pt  - unsatisfactory

For Test II. , one point each correct answer.

For Test III. , if the student listed down:

                (1-5 sets)            --  5pts

                (6 - above sets)  -- 10pts

 

Conclusion

DISCUSSION : 

   SETS -> a well-defined collection of objects — concrete or abstract of any form. The objects comprising the set are called the "elements" or "members"' which are denoted by the Greek letter epsilon. 

Note: 

 a. "Well-defined" means that there is a common characteristic of such elements to enable us to say whether they belong to the set or not.

 b. The members of the set do not necessarily have to be concrete. They maybe ideas, concepts or notions.

 c. It is possible that a set has no members.

 d. We write elements of a set only once.

 

  **Some Basic Notations**

          €                   - is an element of

         U                   - universal set

     A, B, ... Z          - to denote a set

         =                   - is equal to

      <—>                 - is equivalent to

        { }                   - null or empty set

         n                   - cardinality 

 

 *** Sets can also be visible around us. For example, Sala Set.

We can denote the Sala set to be capital letter S.

     = { sofa, tables, chairs, pillows, ...}

Credits

Alimondo M. S., Buasen J. A., Fulwani DL. A., Ocampo P. S., Oryan S. L., Pakipac K. B., Palasi F. D., and Toledo M. B. 2016. Course Manual in College Algebra.