집합의 뜻과 포함 관계

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 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.

For each of the following sets, use English to describe the set and when appropriate, use the roster method to specify all of the elements of the set.

$\left\{ \left. x \in \mathbb{R} \right| -3 \leq x \leq 5 \right\}$

For each of the following sets, use English to describe the set and when appropriate, use the roster method to specify all of the elements of the set.

$\left\{ \left. x \in \mathbb{Z} \right| -3 \leq x \leq 5 \right\}$

For each of the following sets, use English to describe the set and when appropriate, use the roster method to specify all of the elements of the set.

$\left\{ \left. x \in \mathbb{R} \right| x^2 = 16 \right\}$

For each of the following sets, use English to describe the set and when appropriate, use the roster method to specify all of the elements of the set.

$\left\{ \left. x \in \mathbb{R} \right| x^2 + 16 = 0 \right\}$

For each of the following sets, use English to describe the set and when appropriate, use the roster method to specify all of the elements of the set.

$\left\{ \left. x \in \mathbb{Z} \right| x \text{ is odd } \right\}$

For each of the following sets, use English to describe the set and when appropriate, use the roster method to specify all of the elements of the set.

$\left\{ \left. x \in \mathbb{R} \right| 3x - 4 \geq 17 \right\}$

Let the universal set be $U = \left\{ {1,2,3,4,5,6} \right\}$, and let

$$A = \left\{ {1,2,4} \right\}\!, B = \left\{ {1,2,3,5} \right\}\!, C = \left\{ {\left. {x \in U} \right|x^2 \leq 2} \right\}\!$$

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In each of the following, fill in the blank with one or more of the symbols $\subset, \\ \subseteq, =, \ne, \in ,\text{ or } \notin$ so that the resulting statement is true. For each blank, include all symbols that result in a true statement. If none of these symbols makes a true statement, write nothing in the blank.

$A$_____$B$

Let the universal set be $U = \left\{ {1,2,3,4,5,6} \right\}$, and let

$$A = \left\{ {1,2,4} \right\}\!, B = \left\{ {1,2,3,5} \right\}\!, C = \left\{ {\left. {x \in U} \right|x^2 \leq 2} \right\}\!$$

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In each of the following, fill in the blank with one or more of the symbols $\subset, \\ \subseteq, =, \ne, \in ,\text{ or } \notin$ so that the resulting statement is true. For each blank, include all symbols that result in a true statement. If none of these symbols makes a true statement, write nothing in the blank.

5_____$B$

Let the universal set be $U = \left\{ {1,2,3,4,5,6} \right\}$, and let

$$A = \left\{ {1,2,4} \right\}\!, B = \left\{ {1,2,3,5} \right\}\!, C = \left\{ {\left. {x \in U} \right|x^2 \leq 2} \right\}\!$$

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In each of the following, fill in the blank with one or more of the symbols $\subset, \\ \subseteq, =, \ne, \in ,\text{ or } \notin$ so that the resulting statement is true. For each blank, include all symbols that result in a true statement. If none of these symbols makes a true statement, write nothing in the blank.

$A$_____$C$

Let the universal set be $U = \left\{ {1,2,3,4,5,6} \right\}$, and let

$$A = \left\{ {1,2,4} \right\}\!, B = \left\{ {1,2,3,5} \right\}\!, C = \left\{ {\left. {x \in U} \right|x^2 \leq 2} \right\}\!$$

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In each of the following, fill in the blank with one or more of the symbols $\subset, \\ \subseteq, =, \ne, \in ,\text{ or } \notin$ so that the resulting statement is true. For each blank, include all symbols that result in a true statement. If none of these symbols makes a true statement, write nothing in the blank.

$\left\{ {1, 2} \right\}$_____$A$

Let the universal set be $U = \left\{ {1,2,3,4,5,6} \right\}$, and let

$$A = \left\{ {1,2,4} \right\}\!, B = \left\{ {1,2,3,5} \right\}\!, C = \left\{ {\left. {x \in U} \right|x^2 \leq 2} \right\}\!$$

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In each of the following, fill in the blank with one or more of the symbols $\subset, \\ \subseteq, =, \ne, \in ,\text{ or } \notin$ so that the resulting statement is true. For each blank, include all symbols that result in a true statement. If none of these symbols makes a true statement, write nothing in the blank.

6_____$A$

Let the universal set be $U = \left\{ {1,2,3,4,5,6} \right\}$, and let

$$A = \left\{ {1,2,4} \right\}\!, B = \left\{ {1,2,3,5} \right\}\!, C = \left\{ {\left. {x \in U} \right|x^2 \leq 2} \right\}\!$$

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In each of the following, fill in the blank with one or more of the symbols $\subset, \\ \subseteq, =, \ne, \in ,\text{ or } \notin$ so that the resulting statement is true. For each blank, include all symbols that result in a true statement. If none of these symbols makes a true statement, write nothing in the blank.

$\emptyset$_____$A$

Let the universal set be $U = \left\{ {1,2,3,4,5,6} \right\}$, and let

$$A = \left\{ {1,2,4} \right\}\!, B = \left\{ {1,2,3,5} \right\}\!, C = \left\{ {\left. {x \in U} \right|x^2 \leq 2} \right\}\!$$

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In each of the following, fill in the blank with one or more of the symbols $\subset, \\ \subseteq, =, \ne, \in ,\text{ or } \notin$ so that the resulting statement is true. For each blank, include all symbols that result in a true statement. If none of these symbols makes a true statement, write nothing in the blank.

$\left\{ 5 \right\}$_____$B$