Section 2.1 The Nature of Sets
3 ways to describe a set.
1. Descriptive 2. Roster 3. Set-builder Notation
The following sets are given. A = {1,2,3,4,5} B = {0,1,2,3,4} Are the sets equal? Are the sets equivalent?
1. No 2. Yes
Fill in the blank so that the resulting statement is true. The set {California, Colorado, Connecticut} is expressed using __________. The set {x|x is a U.S.state whose name begins with the letter C} is expressed using _________.
1. The Roster Method 2. Set-Builder Notation
Fill in the blanks. A set that contains no elements is called the _______ set and is represented by _______.
1. empty/null set 2. { } or ∅
Determine whether the given statement is true or false. 28 ∈ {13,15,17,...,31}
False because 28 is an even number and on the list there is odd numbers being displayed.
Determine whether the statement is true or false. 14 ∈ {18,19,20,...,31}
False, because 14 is not a natural number greater than or equal to 18 and less than or equal to 31.
Find the cardinal number for the given set. A = {9, 14, 19, ... ,59}
The cardinal number is 11.
Find the cardinal number for the given set. A = {12, 18, 24, 30}
The cardinal number is 4.
Determine if the collection is not well defined and therefore is not a set. The collection of the five worst U.S. parks.
The collection is not well defined and therefore it is not a set.
Determine if the collection is not well defined and therefore is not a set. The collection of current MLB players.
The collection is well defined and therefore it is a set.
Determine whether the set is finite or infinite. {x | x∈N and x ≤ 13,000, 000}
The set is finite because cardinality is either zero or a natural number.
Determine whether the set is finite or infinite. The set of natural numbers less than 17.
The set is finite with a cardinality of 16.
Determine if the set is the empty set. {x | x < 4 and x > 15}
The set is the empty set.
Determine if the set is the empty set. {x | x is a woman who voted in the U.S. before 1800}
The set is the empty set.
Write a description of the set. {Mercury comma Mars}
The set of planet that begin with M.
Determine whether the given statement is true or false. 13 ∉ {1,2,3,...,7}
True because the list stops at 7 and doesn't continue up to 13. It is true because 13 is not a member of the list.
Answer the following questions about the given sets. *a*. Are the sets equivalent? Explain. *b*.Are the sets equal? Explain. A = {3, 3, 3, 5, 5, 7, 9, 11} B = {11, 9, 7, 5, 3}
a. The sets are equivalent because n(A)=n(B). b. the sets are equal because set A contains the exact same elements as set B.
The number of objects in a set. ( how many things are in there)
cardinality
An __________ of a set is a belonging of a set. Draw the symbol/notation.
element the symbol is defined as ∈ => " is element of" ∉ => " is NOT an element of"
The ________ set of zero / no objects. Draw the symbol/notation.
empty the symbol is defined as { } or ∅.
Two sets are __________ if n(A) = n(B) and all elements are equal/same.
equal
Two sets are _________ if n(A) = n(B). (same number of objects)
equivalent
A set is defined as __________ if its cardinality is either zero (empty set) or a natural number.
finite
A __________ is a collection of objects.
set
A set a called __________ if all objects that belong to that set are objectively defined.
well-defined
Express the set using the roster method. { x | x∈N and x < 6}
{1,2,3,4,5}
Express the set using the roster method. The set of odd natural numbers less than 4.
{1,3}
Express the set using the roster method. { x | x∈N and x ≥ 5}
{5,6,7,...}
Give an example of two sets that meet the following condition. If the condition is impossible to satisfy, explain why. The two sets are equivalent and equal.
{x| x∈N and x<5} and {1,2,3,4} The sets {x| x∈N and x < 5} and {1,2,3,4} are equivalent and equal because they both have exactly 4 elements and they both contain the elements 1, 2, 3, and 4.