- The document discusses sets and set notation. It defines basic set concepts like elements, membership using the symbols ∈ and ∉, and cardinality. - It provides examples of sets defined using the roster method by listing elements within curly braces, and asks questions about element membership and cardinality. - Additional methods for defining sets are described, including using a rule or property that elements satisfy, and providing a description of the set's elements.

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NOTE:
• Each member or object in a set is called element of the set.
• We use capital letter to represent the set of objects.
• ∈ is read as “is an element of”
• ∉ is read as “is not an element of”
• The number of elements in a set is called cardinality, Represent
by S = number of elements

10. A = {bonnet, gloves, jacket, jogging pants, socks, scarf}
scarf ∈ A but sando ∉ A
Cardinality:

11. B = {ballpen, pencil, chalk, marker}
is Ballpen ∈ B ?
is crayon ∈ B ?
what is the cardinality of set B ?

12. C = {2, 3, 5, 7, 11, 13, 17, . . .}
is 1 ∈ C ?
is 23 ∈ C ?
what is the cardinality of set B ?

13. D = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}
is 1 ∈ D ?
is 12 ∉ D ?
what is the cardinality of set B ?

14. C = {1, 2, 3 ,4 ,5 ,6 ,7, …}
D = {2, 4, 6, 8, 10}
E = {3, 6, 9, 12, 15, …}
F = {1, 3, 5, 7, 9, 11, 13}
Sets of counting numbers
Sets of odd numbers greater
than 2 but less than 14
Sets of multiples of 3
Sets of even numbers
between 0 and 12
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15. 
Roster Method or Tabular form
→ in this method, all members of the sets are listed and separated by commas.
The list of elements are enclosed by braces { }
Rule Method or Set-builder Notation
→ in this method, the elements of the set are not listed but they are represented
by specific property or general rule which is applicable to all elements.
Description Method
→ in this method, we described the elements of the set and the description of
elements is enclosed by braces { }

16. a set B containing all the days in a week.
B = {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}
B = {x|x is the day in a week}
Tuesday ∈ {days in a week}

17. a set G containing of all even numbers.
G = {0, 2, 4, 6, 8, 10, … }
G = {x|x is an even numbers}
100 ∈ {all even numbers}

18. a set M are months in a year containing letter J.

19. a set M are months in a year containing letter J.
M = {January, June, July}
M = {x|x is a month in year containing letter J}
June ∈ {months in year containing letter J}
January ∈ {months in year containing letter J}
July ∈ {months in year containing letter J}