집합의 연산

Use the definitions of set intersection, set union, and set difference to write useful negations of these definitions. That is, complete each of the following sentences

$x \notin A \cap B$ if and only if $\ldots$.

Use the definitions of set intersection, set union, and set difference to write useful negations of these definitions. That is, complete each of the following sentences

$x \notin A \cup B$ if and only if $\ldots$.

Use the definitions of set intersection, set union, and set difference to write useful negations of these definitions. That is, complete each of the following sentences

$x \notin A - B$ if and only if $\ldots$.

Let $U = \left\{ {1,2,3,4,5,6,7,8,9,10} \right\}$, and let

$$\begin{aligned}A & = \left\{ {3,4,5,6,7} \right\}\!, & B & = \left\{ {1,5,7,9} \right\}\!, \\ C & = \left\{ {3,6,9} \right\}\!, & D & = \left\{ {2,4,6,8} \right\}\!\end{aligned}$$

. Use the roster method to list all of the elements of each of the following sets.

$A \cap B$

Let $U = \left\{ {1,2,3,4,5,6,7,8,9,10} \right\}$, and let

$$\begin{aligned}A & = \left\{ {3,4,5,6,7} \right\}\!, & B & = \left\{ {1,5,7,9} \right\}\!, \\ C & = \left\{ {3,6,9} \right\}\!, & D & = \left\{ {2,4,6,8} \right\}\!\end{aligned}$$

. Use the roster method to list all of the elements of each of the following sets.

$A \cup B$

Let $U = \left\{ {1,2,3,4,5,6,7,8,9,10} \right\}$, and let

$$\begin{aligned}A & = \left\{ {3,4,5,6,7} \right\}\!, & B & = \left\{ {1,5,7,9} \right\}\!, \\ C & = \left\{ {3,6,9} \right\}\!, & D & = \left\{ {2,4,6,8} \right\}\!\end{aligned}$$

. Use the roster method to list all of the elements of each of the following sets.

$\left( {A \cup B} \right)^c$

Let $U = \left\{ {1,2,3,4,5,6,7,8,9,10} \right\}$, and let

$$\begin{aligned}A & = \left\{ {3,4,5,6,7} \right\}\!, & B & = \left\{ {1,5,7,9} \right\}\!, \\ C & = \left\{ {3,6,9} \right\}\!, & D & = \left\{ {2,4,6,8} \right\}\!\end{aligned}$$

. Use the roster method to list all of the elements of each of the following sets.

$A^c \cap B^c$

Let $U = \left\{ {1,2,3,4,5,6,7,8,9,10} \right\}$, and let

$$\begin{aligned}A & = \left\{ {3,4,5,6,7} \right\}\!, & B & = \left\{ {1,5,7,9} \right\}\!, \\ C & = \left\{ {3,6,9} \right\}\!, & D & = \left\{ {2,4,6,8} \right\}\!\end{aligned}$$

. Use the roster method to list all of the elements of each of the following sets.

$\left( {A \cup B} \right) \cap C$

Let $U = \left\{ {1,2,3,4,5,6,7,8,9,10} \right\}$, and let

$$\begin{aligned}A & = \left\{ {3,4,5,6,7} \right\}\!, & B & = \left\{ {1,5,7,9} \right\}\!, \\ C & = \left\{ {3,6,9} \right\}\!, & D & = \left\{ {2,4,6,8} \right\}\!\end{aligned}$$

. Use the roster method to list all of the elements of each of the following sets.

$A \cap C$

Let $U = \left\{ {1,2,3,4,5,6,7,8,9,10} \right\}$, and let

$$\begin{aligned}A & = \left\{ {3,4,5,6,7} \right\}\!, & B & = \left\{ {1,5,7,9} \right\}\!, \\ C & = \left\{ {3,6,9} \right\}\!, & D & = \left\{ {2,4,6,8} \right\}\!\end{aligned}$$

. Use the roster method to list all of the elements of each of the following sets.

$B \cap C$

Let $U = \left\{ {1,2,3,4,5,6,7,8,9,10} \right\}$, and let

$$\begin{aligned}A & = \left\{ {3,4,5,6,7} \right\}\!, & B & = \left\{ {1,5,7,9} \right\}\!, \\ C & = \left\{ {3,6,9} \right\}\!, & D & = \left\{ {2,4,6,8} \right\}\!\end{aligned}$$

. Use the roster method to list all of the elements of each of the following sets.

$\left( {A \cap C} \right) \cup \left( {B \cap C} \right)$

Let $U = \left\{ {1,2,3,4,5,6,7,8,9,10} \right\}$, and let

$$\begin{aligned}A & = \left\{ {3,4,5,6,7} \right\}\!, & B & = \left\{ {1,5,7,9} \right\}\!, \\ C & = \left\{ {3,6,9} \right\}\!, & D & = \left\{ {2,4,6,8} \right\}\!\end{aligned}$$

. Use the roster method to list all of the elements of each of the following sets.

$B \cap D$

Let $U = \left\{ {1,2,3,4,5,6,7,8,9,10} \right\}$, and let

$$\begin{aligned}A & = \left\{ {3,4,5,6,7} \right\}\!, & B & = \left\{ {1,5,7,9} \right\}\!, \\ C & = \left\{ {3,6,9} \right\}\!, & D & = \left\{ {2,4,6,8} \right\}\!\end{aligned}$$

. Use the roster method to list all of the elements of each of the following sets.

$\left( {B \cap D} \right)^c$

Let $U = \left\{ {1,2,3,4,5,6,7,8,9,10} \right\}$, and let

$$\begin{aligned}A & = \left\{ {3,4,5,6,7} \right\}\!, & B & = \left\{ {1,5,7,9} \right\}\!, \\ C & = \left\{ {3,6,9} \right\}\!, & D & = \left\{ {2,4,6,8} \right\}\!\end{aligned}$$

. Use the roster method to list all of the elements of each of the following sets.

$A - D$

Let $U = \left\{ {1,2,3,4,5,6,7,8,9,10} \right\}$, and let

$$\begin{aligned}A & = \left\{ {3,4,5,6,7} \right\}\!, & B & = \left\{ {1,5,7,9} \right\}\!, \\ C & = \left\{ {3,6,9} \right\}\!, & D & = \left\{ {2,4,6,8} \right\}\!\end{aligned}$$

. Use the roster method to list all of the elements of each of the following sets.

$B - D$

Let $U = \left\{ {1,2,3,4,5,6,7,8,9,10} \right\}$, and let

$$\begin{aligned}A & = \left\{ {3,4,5,6,7} \right\}\!, & B & = \left\{ {1,5,7,9} \right\}\!, \\ C & = \left\{ {3,6,9} \right\}\!, & D & = \left\{ {2,4,6,8} \right\}\!\end{aligned}$$

. Use the roster method to list all of the elements of each of the following sets.

$\left( A - D \right) \cup \left( B - D \right)$

Let $U = \left\{ {1,2,3,4,5,6,7,8,9,10} \right\}$, and let

$$\begin{aligned}A & = \left\{ {3,4,5,6,7} \right\}\!, & B & = \left\{ {1,5,7,9} \right\}\!, \\ C & = \left\{ {3,6,9} \right\}\!, & D & = \left\{ {2,4,6,8} \right\}\!\end{aligned}$$

. Use the roster method to list all of the elements of each of the following sets.

$\left( A \cup B \right) - D$

Let $U = \mathbb{N}$, and let

$$\begin{aligned}A & = \left\{ x \in \mathbb{N} \mid x \geq 7 \right\}\!, & B & = \left\{ x \in \mathbb{N} \mid x \text{ is odd } \right\}\!, \\ C & = \left\{ x \in \mathbb{N} \mid x \text{ is a multiple of 3 } \right\}\!, & D & = \left\{ x \in \mathbb{N} \mid x \text{ is even } \right\}\!\end{aligned}$$

. Use the roster method to list all of the elements of each of the following sets.

$A \cap B$

Let $U = \mathbb{N}$, and let

$$\begin{aligned}A & = \left\{ x \in \mathbb{N} \mid x \geq 7 \right\}\!, & B & = \left\{ x \in \mathbb{N} \mid x \text{ is odd } \right\}\!, \\ C & = \left\{ x \in \mathbb{N} \mid x \text{ is a multiple of 3 } \right\}\!, & D & = \left\{ x \in \mathbb{N} \mid x \text{ is even } \right\}\!\end{aligned}$$

. Use the roster method to list all of the elements of each of the following sets.

$A \cup B$

Let $U = \mathbb{N}$, and let

$$\begin{aligned}A & = \left\{ x \in \mathbb{N} \mid x \geq 7 \right\}\!, & B & = \left\{ x \in \mathbb{N} \mid x \text{ is odd } \right\}\!, \\ C & = \left\{ x \in \mathbb{N} \mid x \text{ is a multiple of 3 } \right\}\!, & D & = \left\{ x \in \mathbb{N} \mid x \text{ is even } \right\}\!\end{aligned}$$

. Use the roster method to list all of the elements of each of the following sets.

$\left( {A \cup B} \right)^c$