집합과 명제 전체 문제

Use the roster method to specify the elements in each of the following sets and then write a sentence in English describing the set.

$\left\{ {x \in \mathbb{Z}} \mid x^2 \lt 25 \right\}$

Use the roster method to specify the elements in each of the following sets and then write a sentence in English describing the set.

$\left\{ {x \in \mathbb{N}} \mid x^2 \lt 25 \right\}$

Use the roster method to specify the elements in each of the following sets and then write a sentence in English describing the set.

$\left\{ {y \in \mathbb{Q}} \mid \left| {y - 2} \right| = 2.5 \right\}$

Use the roster method to specify the elements in each of the following sets and then write a sentence in English describing the set.

$\left\{ {y \in \mathbb{Z}} \mid \left| {y - 2} \right| \leq 2.5 \right\}$

Each of the following sets is defined using the roster method.

$$\begin{aligned}A & = \left\{1, 4, 9, 16, 25, \ldots \right\} & B & = \left\{\ldots, -\pi^4, -\pi^3, -\pi^2, -\pi, -1 \right\} \\ C & = \left\{3, 9, 15, 21, 27, \ldots \right\} & D & = \left\{0, 4, 8, \ldots, 96, 100 \right\}\end{aligned}$$

Determine four elements of each set other than the ones listed using the roster method.

Each of the following sets is defined using the roster method.

$$\begin{aligned}A & = \left\{1, 4, 9, 16, 25, \ldots \right\} & B & = \left\{\ldots, -\pi^4, -\pi^3, -\pi^2, -\pi, -1 \right\} \\ C & = \left\{3, 9, 15, 21, 27, \ldots \right\} & D & = \left\{0, 4, 8, \ldots, 96, 100 \right\}\end{aligned}$$

Use set builder notation to describe each set.

Let $A = \left\{ x \in \mathbb{R} \mid x\left( {x + 2} \right)^2 \left( x - \frac{3}{2} \right) = 0 \right\}$. Which of the following sets are equal to the set $A$ and which are subsets of $A$?

$\left\{ { - 2, 0,3} \right\}$

Let $A = \left\{ x \in \mathbb{R} \mid x\left( {x + 2} \right)^2 \left( x - \frac{3}{2} \right) = 0 \right\}$. Which of the following sets are equal to the set $A$ and which are subsets of $A$?

$\left\{ {\dfrac{3}{2}, - 2,0} \right\}$

Let $A = \left\{ x \in \mathbb{R} \mid x\left( {x + 2} \right)^2 \left( x - \frac{3}{2} \right) = 0 \right\}$. Which of the following sets are equal to the set $A$ and which are subsets of $A$?

$\left\{ { - 2, - 2,0,\dfrac{3}{2}} \right\}$

Let $A = \left\{ x \in \mathbb{R} \mid x\left( {x + 2} \right)^2 \left( x - \frac{3}{2} \right) = 0 \right\}$. Which of the following sets are equal to the set $A$ and which are subsets of $A$?

$\left\{ { - 2, \dfrac{3}{2}} \right\}$

Use the roster method to specify the truth set for each of the following open sentences. The universal set for each open sentence is the set of integers $\mathbb{Z}$.

$n + 7 = 4$.

Use the roster method to specify the truth set for each of the following open sentences. The universal set for each open sentence is the set of integers $\mathbb{Z}$.

$n^2 = 64$.

Use the roster method to specify the truth set for each of the following open sentences. The universal set for each open sentence is the set of integers $\mathbb{Z}$.

$\sqrt{n} \in \mathbb{N}$ and $n$ is less than 50.

Use the roster method to specify the truth set for each of the following open sentences. The universal set for each open sentence is the set of integers $\mathbb{Z}$.

$n$ is an odd integer that is greater than 2 and less than 14.

Use the roster method to specify the truth set for each of the following open sentences. The universal set for each open sentence is the set of integers $\mathbb{Z}$.

$n$ is an even integer that is greater than 10.

Use set builder notation to specify the following sets:

The set of all integers greater than or equal to 5.

Use set builder notation to specify the following sets:

The set of all even integers.

Use set builder notation to specify the following sets:

The set of all positive rational numbers.

Use set builder notation to specify the following sets:

The set of all real numbers greater than 1 and less than 7.

Use set builder notation to specify the following sets:

The set of all real numbers whose square is greater than 10.