Math 7. Lesson 1SETS

Name the set of all fingers in a hand.

Name the set of all fingers in a hand.

ThumbIndex finger

Middle fingerRing fingerLittle finger

OBJECTIVE

•Describe and illustrate well-defined sets.

SET• It is a collection of objects,

called “elements or members” that have something in common

or follow a rule.• In writing sets, it uses curly braces {} with

elements separated by commas.Example:A= {Alicia, Imelda, Ipil, Olutanga, Mabuhay,

Buug, RT Lim, Tungawan, Siay, Naga}

A SET CAN BE REPRESENTED IN 3 WAYS OR FORMS:

1. Descriptive Form2. Set-Builder or Rule Form3. Roster Form or Tabular Form

DESCRIPTIVE FORM Give a verbal description of its

elements It must allow a concise

determination of which elements belong to the set and which elements do not.

DESCRIPTIVE FORM

1. D= {The set of all counting numbers}

2. O= {The set of all vowel letters}3. G= {The set of all numbers less

than 5}

SET-BUILDER FORM/ RULE FORM It is a notation for describing a

set by indicating the properties that its members must satisfy.

“I” or “:” is read as “such that”

SET-BUILDER FORM/ RULE FORM

1) D= {x|x is a letter in the word MANILA}

2) O= {x|x is a vowel letter}3) G= {x|x is an even number less

than 50}

ROSTER FORM / TABULAR FORM Listing of all elements of a set

inside a pair of curly braces { }1) C={ a, e, i, o, u }2) A={2, 4, 6, 8, 10}3) T= {1, 3, 5, 7, 9}

ROSTER FORM / TABULAR FORM Each element must be listed

exactly ONCE. Set elements can be written in

ANY ORDER. All elements must be written

inside the braces.

Points to Remember Capital letters are used to

denote sets. Lowercase letters are used to

denote elements of sets. Curly braces { } denote the

elements in the set.

Sets in Different Forms DESCRIPTIVE FORM SET-BUILDER FORM ROSTER FORM

A= {The set of all vowels in English Alphabet}

A={x|x is a vowel in English alphabet}

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

B={ The set of all odd positive integers less than or equal to 17}

B={x|x is an odd number less than or equal to 17}

B={1,3,5,7,9,11,13,15,17}

C= {The set of numbers greater than 9 but less than 21}

C= {x|x is a number greater than 9 but less than 21}

C= {10,11,12,13, 14, 15, 16, 17, 18,19, 20}

TRY THIS WITH YOUR SEAT MATE

Write the following using the 3 forms of set notation:

1. Days of the week2. Months of the year3. Whole numbers from 25 to 30

ELEMENT OF A SET

The object that belongs to a set is called an “element” or member of the set.

The symbol ϵ is read as “is an element of”

Example: A= {1, 2, 3, 4, 5}2 ϵ A or “2 is an element of A”5 ϵ A or “5 is an element of A”

Determine if the given item is an element of the set or not.

SET ITEM Is an element or not?

R= {2, 4, 6, 8 } 2 2 ϵ RR= {2, 4, 6, 8 } 10 1. S= {2, 4, 6, 8, 10} 10 2.D= { English Alphabet} m 3.D= { English Alphabet} Ʃ 4.X= { Numbers less than 0} -2 5.

Let’s EVALUATE your learning.

List down the elements of each set using Roster Method.

1. L={the first 10 counting numbers}2. O= { x|x are whole numbers less than 10 but

greater than 0}To answer 3 and 4, let V={ 11, 12, 13, 14, 15, 16}3. List down the elements that are odd numbers.4. List down the elements that are even

numbers.