집합의 뜻과 포함 관계

다음 연습문제에서 주어진 각 집합의 부분집합의 개수를 구하세요.

$\{a,b,c,\ldots ,z\}$

다음 문제에서 주어진 각 집합의 부분집합의 개수를 구하세요.

서로 다른 숫자 5개, 서로 다른 문자 4개, 서로 다른 기호 3개를 원소로 갖는 집합

다음 문제에서 주어진 각 집합의 부분집합의 개수를 구하세요.

2부터 28까지의 짝수의 집합

다음 문제에서 주어진 각 집합의 부분집합의 개수를 구하세요.

1과 100 사이의 두 자리 수 중 숫자 0을 포함하는 수의 집합

집합 $A$ 의 부분집합이 2,048개라고 합시다. $A$ 에 들어 있는 서로 다른 원소는 몇 개인지 구하세요.

집합 $\{1,\,3,\,5,\,\ldots ,\,99\}$ 의 부분집합은 모두 몇 개인지 구하세요.

Let $A = \{ -4, -2, 0, 2, 4, 6, 8, \ldots \}$. Use correct set notation to indicate which of the following integers are in the set $A$ and which are not in the set $A$. For example, we could write $6 \in A$ and $5 \notin A$.

$$10 \qquad 22 \qquad 13 \qquad -3 \qquad 0 \qquad -12$$

Use correct set notation (using $=$ or $\subseteq$) to indicate which of the following sets are equal and which are subsets of one of the other sets.

$$\begin{aligned}A & = \{3, 6, 9 \} & B & = \{6, 9, 3, 6 \} \\ C & = \{3, 6, 9, \ldots \} & D & = \{ 3, 6, 7, 9 \} \\ E & = \{9, 12, 15, \ldots \} & F & = \{9, 7, 6, 2 \}\end{aligned}$$

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

$$\begin{aligned}A & = \left\{1, 5, 9, 13, \ldots \right\} \\ B & = \left\{\ldots, -8, -6, -4, -2 , 0 \right\} \\ C & = \left\{\sqrt{2}, \left( \sqrt{2}\right)^3, \left( \sqrt{2}\right)^5, \ldots \,\right\} \\ D & = \left\{1, 3, 9, 27, \ldots \right\}\end{aligned}$$

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.

$$\begin{aligned}A & = \left\{1, 5, 9, 13, \ldots \right\} \\ B & = \left\{\ldots, -8, -6, -4, -2 , 0 \right\} \\ C & = \left\{\sqrt{2}, \left( \sqrt{2}\right)^3, \left( \sqrt{2}\right)^5, \ldots \,\right\} \\ D & = \left\{1, 3, 9, 27, \ldots \right\}\end{aligned}$$

Use set builder notation to describe each set.

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

$\left\{ x \in \mathbb{R} \mid 2x^2 + 3x - 2 = 0 \right\}$

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

$\left\{ {x \in \mathbb{Z}} \mid 2x^2 + 3x - 2 = 0 \right\}$

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

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

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 $A$?

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