S
S
NS
NS
P={x|x is a positive integers greater than 6}
INTRODUCTION TO SETS
Mathematicians place objects with similar properties in groups called sets. A set is a list or
collection of well-defined objects or ideas. The objects in a set are called the elements or members of the
set.
EXAMPLE: Which of the following collections are sets?
a) the past presidents of a country
b) good players who have played for the national team
SOLUTION: The first collection is a set but the second one is not since we are not given the criteria
whether the player is good or not.
Sets can be defined either of the following ways: (1) a verbal description, (2) the roster method, a
listing of the members separated by commas, with braces { } used to enclose the list of elements and (3)
the rule method or set-builder notation.
EXAMPLE: Write “the set of vowels in the alphabet" in roster and set-builder notation.
SOLUTION: Roster Method: {a, e, i, o, u}
Set-builder Notation: {x/x is a vowel in the alphabet} (This set-builder notation is read as " The set
of all x's such that x is a vowel in the alphabet.")
Sets are usually denoted by capital letters such as A, B, C and so on. The symbols " " and " " are
used to indicate that an object is or is not an element of a set respectively. For example, if S represents
the set of all flowers, then rose S and mango S.
Universal set or universe is the set that comprises all elements being considered in a particular
discussion.
A set without elements is called an empty set or null set and is denoted by { } or the symbol ø.
The cardinality of sets refers to the number of elements in a given set.
EXERCISES:
A. Write S if the statement describes a set and NS if not.
____ 1. Current employees of Island City Mall.
____ 2. Interesting books published since 1998.
____ 3. The good-looking men who have played for the national basketball team.
____ 4. The math teachers of Bohol Island State University.
B. Write the following in rule method or set-builder notation.
1. {5, 10, 15, 20}
2. the positive integers greater than 6
C. Write the following in roster method.
1. the five sense organs of the body
2. {x/x is an integer, 5< x <12}
D. Find the cardinality of the following sets.
1. A={ 2, 4, 6, 8, 10}
L={x|x is a multiple of 5}
O={ eyes, ears, nose, tongue, skin }
M={5, 6, 7, 8, 9, 10, 11, 12}
n(A) = 5
n(A) = 6
