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2.1 Basic set concepts.
Section 2.1 Notes Page 1
A set is a collection of objects whose contents can be clearly determined. (Capital letters are
generally used to name sets)
The objects in a set are called the elements or members of the set.
Example:
Word Description; S is the set of states whose names begin with the letter A.
Roster method; S = {Alabama, Alaska, Arizona, Arkansas}
Set- Builder Notation; S = {x|x is a U.S. state whose name begins with the letter A}
The empty set, also called the null set, is the set that contains no elements. The empty set is
represented by { } or ∅.
The symbol ∈ is used to indicate that an object is an element of a set.
The symbol ∉ is used to indicate that an object is not an element of a set.
The set of counting numbers is also called the set of Natural numbers and we represent this set
by the bold face letter N. N = {1, 2, 3, …}
The cardinal number of set A, represented by n(A), is the number of distinct elements in set A.
Set A is equivalent to set B means that set A and set B contain the same number of elements.
If set A and set B can be placed in a one to one correspondence, than A is equivalent to B: n(A)
= n(B)
Set A is a finite set if n(A) = 0 ( that is, A is the empty set) or n(A) is a natural number. S set
whose cardinality is not 0 or a natural number is called an infinite set.
Set A is equal to set B means that set A and set B contain exactly the same elements,
regardless of order or possible repetition of elements. We symbolize the equality of sets A and
B using the statement A = B.
Ex1. Express each set using the roster method.
a) Set C is the set of U.S. coins with a value of less than a dollar.
b) Set M is the set of months beginning with the letter A.
c) Set O is the set of a positive odd number less than 10.
d) E = {X|X ∈ N and x is even}
Ex2. Which one of the following is the empty set?
a) {0}
b) 0
c) {X|X is a number less than 4 or greater than 10}
d) {X|X is a square with exactly three sides}
e) {∅}
Ex3. Determine whether each statement is true of false:
a) r ∈ {a, b, c, ….,z}
b) 7 ∉ {1, 2, 3, 4, 5}
c) {a} ∈ {a, b}
d) {Monday} ∈ {X|X is an day of the week}
Ex4. Find the cardinal number of each of the following sets:
a) A = {7, 9, 11, 13}
b) B = {0}
c) C = {13, 14, 15, …., 22, 23}
d) ∅
e) D = {871}
Section 2.1 Notes Page 2
Section 2.1 Notes Page 3
Ex5. Determine whether each statement is true or false:
a) {4, 8, 9} = {8, 9, 4}
b) {1, 3, 5} = {0, 1, 3, 5}
c) {4, 5} = {5, 4, ∅}