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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, …}
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