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

13. Example: All the planets in the solar system elements: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus and Neptune

14. Two Kinds of Sets a. Finite sets If 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

15. Two Kinds of Sets b. infinite sets there is no exact number that describes exactly how many elements it contains Example: The set of all real numbers

16. c. Empty or null set The set containing no elements and denoted by { } or Ø

17. Ways of representing a set a. 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

18. 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. ”

19. 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

20. Ways of representing a set b. 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

21. 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”

22. Exercises: 1.All the positive multiples of 3 2.All the states of the Unites States 3.All even natural numbers

23. 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

24. 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, …}