Chapter 3, Sets and Counting Video Solutions, The Mathematical Palette | Numerade (2024)

What is a set?

What is the listing method of showing the items in a set? Give an example.

What is the descriptive method of showing the items in a set? Give an example.

What is meant by cardinality of a set?

What does it mean if a set $A$ is a subset of set $B$ ?

If $A \subseteq B$ and $B \subseteq A$, what can you say about sets $A$ and $B$ ? Give an example.

What is meant if two finite sets are equivalent?

What is meant if two infinite sets are equivalent?

What does it mean to say that a set is countably infinite?

What is meant by a one-to-one relationship?

Write the set of even whole numbers less than or equal to 10 , using the
a) Descriptive method.
b) Listing method.

In Problems 13-24, Use the sets $T=\{3,6,9,12\}, F=\{5,10,15,20,25\}$, and $I=$ \{all the integers\} to determine whether the subset and element symbols are used correctly. If the symbol is being used correctly, is the statement true? If not, write a true statement. If the symbol is being used incorrectly, write a true statement using the correct symbol.
$F \subset I$

Use the sets $T=\{3,6,9,12\}, F=\{5,10,15,20,25\}$, and $I=$ \{all the integers\} to determine whether the subset and element symbols are used correctly. If the symbol is being used correctly, is the statement true? If not, write a true statement. If the symbol is being used incorrectly, write a true statement using the correct symbol.
$I \subset F$

Use the sets $T=\{3,6,9,12\}, F=\{5,10,15,20,25\}$, and $I=$ \{all the integers\} to determine whether the subset and element symbols are used correctly. If the symbol is being used correctly, is the statement true? If not, write a true statement. If the symbol is being used incorrectly, write a true statement using the correct symbol.
$T \subset F$

Use the sets $T=\{3,6,9,12\}, F=\{5,10,15,20,25\}$, and $I=$ \{all the integers\} to determine whether the subset and element symbols are used correctly. If the symbol is being used correctly, is the statement true? If not, write a true statement. If the symbol is being used incorrectly, write a true statement using the correct symbol.
$T \subset I$

Use the sets $T=\{3,6,9,12\}, F=\{5,10,15,20,25\}$, and $I=$ \{all the integers\} to determine whether the subset and element symbols are used correctly. If the symbol is being used correctly, is the statement true? If not, write a true statement. If the symbol is being used incorrectly, write a true statement using the correct symbol.
$5 \subset I$

Use the sets $T=\{3,6,9,12\}, F=\{5,10,15,20,25\}$, and $I=$ \{all the integers\} to determine whether the subset and element symbols are used correctly. If the symbol is being used correctly, is the statement true? If not, write a true statement. If the symbol is being used incorrectly, write a true statement using the correct symbol.
$5 \subset F$

Use the sets $T=\{3,6,9,12\}, F=\{5,10,15,20,25\}$, and $I=$ \{all the integers\} to determine whether the subset and element symbols are used correctly. If the symbol is being used correctly, is the statement true? If not, write a true statement. If the symbol is being used incorrectly, write a true statement using the correct symbol.
$5 \notin I$

Use the sets $T=\{3,6,9,12\}, F=\{5,10,15,20,25\}$, and $I=$ \{all the integers\} to determine whether the subset and element symbols are used correctly. If the symbol is being used correctly, is the statement true? If not, write a true statement. If the symbol is being used incorrectly, write a true statement using the correct symbol.
$5 \notin F$

Use the sets $T=\{3,6,9,12\}, F=\{5,10,15,20,25\}$, and $I=$ \{all the integers\} to determine whether the subset and element symbols are used correctly. If the symbol is being used correctly, is the statement true? If not, write a true statement. If the symbol is being used incorrectly, write a true statement using the correct symbol.
$5 \in I$

Use the sets $T=\{3,6,9,12\}, F=\{5,10,15,20,25\}$, and $I=$ \{all the integers\} to determine whether the subset and element symbols are used correctly. If the symbol is being used correctly, is the statement true? If not, write a true statement. If the symbol is being used incorrectly, write a true statement using the correct symbol.
$5 \notin T$

Use the sets $T=\{3,6,9,12\}, F=\{5,10,15,20,25\}$, and $I=$ \{all the integers\} to determine whether the subset and element symbols are used correctly. If the symbol is being used correctly, is the statement true? If not, write a true statement. If the symbol is being used incorrectly, write a true statement using the correct symbol.
$F \in I$

Use the sets $T=\{3,6,9,12\}, F=\{5,10,15,20,25\}$, and $I=$ \{all the integers\} to determine whether the subset and element symbols are used correctly. If the symbol is being used correctly, is the statement true? If not, write a true statement. If the symbol is being used incorrectly, write a true statement using the correct symbol.
$T \notin I$

Show that the set $F=\{5,10,15,20,25, \ldots\}$ is countably infinite. What is the mathematical relationship that shows the one-to-one correspondence?

Show that the set $F=\{1,5,9,13,17, \ldots\}$ is countably infinite. What is the mathematical relationship that shows the one-to-one correspondence?

Show that the set $F=\{1,4,9,16,25,36, \ldots\}$ is countably infinite. What is the mathematical relationship that shows the one-to-one correspondence?

Show that the set $F=\{1,3,9,27,81, \ldots\}$ is countably infinite. What is the mathematical relationship that shows the one-to-one correspondence?

Use the listing method to create a set $A$ of the states that border Indiana.

Use the listing method to create a set $E$ of the countries that border France.

Use the listing method to create a set $N$ of the countries that border South Africa and are north of the equator.

Use the listing method to create a set $S$ of the states that border California and are also touching the Atlantic Ocean.

Let $P$ be the set of U.S. Presidents in the years $1940-2003$. Find $n(P)$.

Let $C$ be the set of state capitals in the United States. Find $n(C)$.

Let $B$ be the set of major league baseball teams as of 2003. Find $n(B)$.

Let $J$ be the set of current U.S. Supreme Court justices. Find $n(J)$.

Show that the sets $R=\{3,6,9,12,15, \ldots\}$ and $S=\{1,3,9,27,81, \ldots\}$ are equivalent.

Show that the sets $R=\{1,2,6,24,120,720, \ldots\}$ and $S=\{1,3,5,7,9,11, \ldots\}$ are equivalent.