Download Set

Prepared by:
Still John F. Reyes



Set- is a collection or aggregate of definite,
distinct objects.
A well-defined set means that it is possible to
determine whether an object belongs to a
given set.
Elements of a Set- the objects or members of
a set.
• Symbol: ε (epsilon)- use to denote the element of a
set. Ex: r ε A
ε – use to denote that an element is not an
element of the given set. Ex: b ε A
Ex. of well-defined sets (defined)
1. Set of ace cards
2. Colors of the rainbow
3. Days of the week
Ex. of not well-defined sets (undefined)
1. Set of cards
2. Set of books
3. Set of beautiful women in Asia
Different symbols are used when dealing with
sets:
1. A pair of braces { } – is used to represent the
idea of a set.
2. Capital letters of the English alphabet – are
used to name sets.
Example:
A = { a, b, c, d, e }
B = { 2, 4, 6, 8, 10 }

1. Roster or Tabular Method – listing all the
elements, enclosed it in braces and
separated by comma.
Ex:
C = { a, b, c }
B = { 1, 2, 3, 4, 5 }
2. Rule Method – a conditional way of listing
method by writing and description using a
particular variable.
 set builder notation – a modification of the rule
method.

Examples:
Rule
Set-builder
1. A = { counting numbers less than
5}
A = { x/x is a counting number less
than 5 }
2. B = { days of the week that begin
with letter S }
B = { x/x is a day of the week
beginning with letter S }
 The
symbol ( / ) means “wherein” or “such
that.”


Subset – it is a part of a given set.
Two kinds of subset:
Proper Subset – a part of a set, symbol ( ⊂ )
Improper Subset – the given set is equal to
that set, symbol ( ⊆ )
Number of Subsets of a Given Set:
- If a set contains n number of elements then
the number of subsets is 2ⁿ
1.
2.
3.
4.
Empty or Null Set – sets having no elements.
Symbol: { } or ∅
Universal Set (U) – also called the general
set, is the sum of all sets or the totality of
elements under consideration or a particular
discussion.
Unit Set – set having only one element.
Finite Set – sets having a limited or
countable number of elements.
5.
6.
7.
8.
9.
Infinite Set – sets having an unlimited or
uncountable number of elements.
Equal Sets – sets having the same elements.
Symbol: (=)
Equivalent Sets – sets having the same
number of elements. Symbol: (~)
Joint Sets – sets that have elements in
common.
Disjoint Sets – sets that have no elements in
common.



It is a graphical representation, usually
circular in nature. It is one way of showing
the relationships of two or more sets by the
use of pictures.
This method was developed by John Venn
(1834-1883) thus, the name Venn Diagram.
It consists of a rectangle representing the
universal set and circles that represent the
sets. Sometimes, circles can also represent
the universal set.
A
B
a, b, c
d, e, f
1.
2.
3.
4.
Union – it shows the unity of two or more
sets. It is the joining of sets. ( ∪ )
Intersection – it shows the intersection of
the common elements of sets. ( ∩ )
Complement of a Set – it is the set whose
elements are in the universal set but not in
a set or a given set. ( ʼ )
Difference – set of elements found in a set
but not belong or found in other set. ( - )