Section 2.1 The Nature of Sets

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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.


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