3. SET
• a set is a well-defined group or collection of objects.
4. WELL-DEFINED or NOT
• The vowels in the English alphabet.
• The months of a year.
• Even numbers from 0 to 10.
• Group of intelligen students.
• List of beautiful students in your school.
• A basket of different delicious fruits.
5. WELL-DEFINED or NOT
• Primary color.
• A popular actor.
• Great philosopher.
• Colors of the rainbow.
6. SET
• a set is a well-defined group or collection of objects.
• each object in a set is called an element denoted by the
symbol ϵ.
• sets are named by any capital letters.
• elements can only be written once and are enclosed by
braces and are separated by commas.
7. EXAMPLE 1:
Set A is the set of all even integers.
A = {2, 4, 6, 8, 10, 12, ...}
2 ϵ A (2 is an element of set A)
1 ϵ A (1 is not an element os set A)
8. EXAMPLE 2:
Set B is the set of weekdays.
B = {Monday, Tuesday, Wednesday, Thursday, Friday}
Tuesday _____ B
Saturaday _____B
9. EXAMPLES:
Set A is the set of all even integers.
A = {2, 4, 6, 8, 10, 12, ...}
Set B is the set of weekends.
B = {Saturday, Sunday}
10. Finite Set
• a set is a finite set if all the elements of the set can be
listed down.
• is a set with countable elements.
Other examples:
• Set B is the set of natural numbers between 5 and 12.
• C = {1, 2, 3, ..., 9, 10}
11. Infinite Set
• a set is an infinite set if not all the elements can be listed
down.
• is a set with uncountable elements.
Othe exanples:
• Set C is the set of natural numbers.
• D = {2, 3, 5, 7, ...}
12. FINITE vs INFINITE
• G = {letters of the alphabet}
• F = {even numbers greater than 2}
• H = {multiple of 6}
• I = {polar bear lives in Sahara Desert}
13. Null Set/Empty Set
• is a set containing no elements and is denoted by the
symbols { } or Ø.
Other Examples:
• Set E is the set of whole number less than 0.
E = { }
• Set F is the set of cars with two wheels.
F = Ø
14. CARDINALITY
• cardinality of set A denoted by n(A) refers to the number
of elements in a given set.
Examples:
• A = {d, e, f, g, h} n(A) = 5
• Set M is the set of the months in a year. n(A) = 12
• I = {polar bear lives in Sahara Desert} n(A) = 0
• K = {x|x is a counting number} n(K) =
uncountable
16. 1. Verbal Description
• it is a method of describing sets in form of a sentence.
Examples:
• Set A is the set of natural numbers less than 6.
• Set B is the set of distinct letters in the word “kindness”
• Set C is the odd numbers from 3 to 15.
17. 2. Roster/Listing Method
• this method of describing set is done by listing each
elements inside the braces and each element are
separated by commas.
Examples:
• A = {1, 2, 3, 4, 5}
• B = {k, i, n, d, e, s}
• C = {3, 5, 7, 9, 11, 13, 15}
18. 3. Set Bulider/Rule Method
• it is a methos that list the rules that determines whether
the objects is an element of the set rather than the actual
elements.
Examples:
• A = {x|x is a natural number less than 6}
• B = {x|x is a distinct letter in the word “kindness”}
• C = {x|x is an odd number from 3 to 15}
20. Universal Set
• it is the setntains all the elements being considered in a
given situtation. It is denoted by the symbol U.
Example:
A = {1, 3, 5, 7, 9, ...} and B = {2, 4, 6, 8, ...}
U = {1, 2, 3, 4, ...} or U = {x|x is a counting number} or
set U is the set of all counting numbers.
21. Subset
• set A is said to be a subset of set B if every element of A
is also an element of B.
22. 1. Proper Subset
• set A is said to be a proper subset of B if every element of
A is also an element of B and B contains at least one
element which is not in A.
• we symbolize this concept as A⊂B.
23. EXAMPLE:
A = {2, 4}
B = {2, 4, 6}
A⊂B read as set A is a proper subset of set B because
every element of set A is found in set B but there is at least
one element that is in set B but not in set A.
24. EXAMPLE:
A = {2, 4}
B = {2, 4, 6}
B ⊄A read as set B is not a proper subset of set A because
not all the elements of set B are in set A.
25. 2. Improper Subset
• set A is said to be improper subset of B if all the elements
of A is also the elements of B or simply, they are equal
sets.
• we symbolize this concept by A ⊆ B.
26. EXAMPLE:
A = {2, 4, 6}
B = {x|x is an even number less than 8}
A ⊆ B read as set A is an improper subset of set B because
they have the same elements.
