집합과 명제 전체 문제

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.

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.

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

For each of the following statements

• (1) Write the statement in the form of an English sentence that does not use the symbols for quantifiers. - (2) Write the negation of the statement in a symbolic form that does not use the negation symbol. - (3) Write the negation of the statement in the form of an English sentence that does not use the symbols for quantifiers.

$\left( \forall a \in \mathbb{R}\right) \left( a + 0 = a \right)$.

For each of the following statements

• (1) Write the statement in the form of an English sentence that does not use the symbols for quantifiers. - (2) Write the negation of the statement in a symbolic form that does not use the negation symbol. - (3) Write the negation of the statement in the form of an English sentence that does not use the symbols for quantifiers.

$\left( \forall x \in \mathbb{R} \right) \left[ \sin ( {2x} ) = 2 ( {\sin x} ) ( {\cos x} ) \right]$.