Any well-defined collection of objects and each object of the collection is an element or member of the set

Example:

All the planets in the solar systemelements:

Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus and Neptune

Two Kinds of Sets

a. Finite setsIf and only if there is a number that describes exactly how many elements it contains

Example:The set of all the vowels of the alphabet

Two Kinds of Sets

b. infinite setsthere is no exact number that

describes exactly how many elements it contains

Example:The set of all real numbers

c. Empty or null setThe set containing no elements

and denoted by { } or Ø

Ways of representing a seta. Roster notation•If the collection does not contain

a very large number of objects

•All the elements are listed and enclosed them between a pair of braces

Example:All the vowels of the alphabet

A ={ a, e, i, o, u}•Read as “the set whose

elements are a, e, i, o, u.”

Exercises:1.All months of the year

having exactly 30 days

2.All suits in a deck of playing cards

3.The squares of the first four natural numbers

Ways of representing a setb. set-builder notation•If the collection contains a very

large number of objects

•Tells what requirements must be met in order to belong to the set

Example:All the countries in the world

A ={ x| x is a country in the world }•Read as “the set of all x’s such that x is a country in the world”

Exercises:1.All the positive multiples of 3

2.All the states of the Unites States

3.All even natural numbers

Exercises:Represent each set using the roster method.1.All the types of clouds

2.All the distinct letters in the word “Mississippi”

3.All natural numbers less than 5

4.Students in the class who are not from cebu

5.The children of your parents

Exercises:Represent each set using the set-builder notation. identify the set as either finite or infinite.1. {2, 4, 6, 8, 10, …}

2. {Mercury, Earth, Mars, Neptune, …}

3. {5, 10, 15, 20, …}

4. {Macapagal, Garcia, Magsaysay, Quirino, …}

5. {Philippines, Panama, Puerto Rica, …}