Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Which is the set of integers greater than $-4$ and less than or equal to $1$ ? $\newline$ Choices: $\newline$ (A) $\{-4, 0, 1\}$ $\newline$ (B) $\{-3, -2, -1, 0, 1\}$ $\newline$ (C) $\{-4, -3, -2, -1, 0, 1\}$ $\newline$ (D) $\{0, 1\}$

View step-by-step help

View step-by-step help

Set-builder notation

Full solution

Q. Which is the set of integers greater than

-4

and less than or equal to

1

?

\newline

Choices:

\newline

(A)

\{-4, 0, 1\}

\newline

(B)

\{-3, -2, -1, 0, 1\}

\newline

(C)

\{-4, -3, -2, -1, 0, 1\}

\newline

(D)

\{0, 1\}

Identify Range of Integers: Identify the range of integers that satisfy the given conditions. $\newline$ We are looking for integers that are greater than $-4$ and less than or equal to $1$ . This means we need to find all integers that fall between $-4$ (not included) and $1$ (included).
List Satisfying Integers: List the integers that satisfy the first condition (greater than $-4$ ). $\newline$ The integers greater than $-4$ are $-3$ , $-2$ , $-1$ , $0$ , $1$ , $2$ , $3$ , and so on. However, we are only interested in those that are also less than or equal to $1$ .
Apply Second Condition: Apply the second condition ( $\leq 1$ ) to the list from Step $2$ . $\newline$ From the list of integers greater than $-4$ , we select those that are also less than or equal to $1$ , which are $-3$ , $-2$ , $-1$ , $0$ , and $1$ .
Match to Given Choices: Match the resulting set of integers to the given choices. $\newline$ The set of integers that are greater than $-4$ and less than or equal to $1$ is $\{-3, -2, -1, 0, 1\}$ . This corresponds to choice (B).

More problems from Set-builder notation

Question

R = \{-4, 4, 14\}

S = \{2, 12\}

R \cup S

\newline

\newline

\{-4,2,4,12,14\}

\newline

\Phi

\newline

\{2, 4, 12\}

\newline

\{-4, 2\}

Posted 3 months ago

Question

Which is the set of integers greater than or equal to

0

and less than or equal to

6

\newline

\newline

(A)\{1,2,3,4,5,6\}

\newline

(B)\{0,1,2,3,4,5,6\}

\newline

(C)\{\text{null set}\}

\newline

(D)\{1,6\}

Posted 3 months ago

Question

Which is the set of numbers less than

-13

\newline

\newline

\{x|x = -13\}

\newline

\{x|x < -13\}

\newline

\{x|x > -13\}

\newline

\{x|x \leq -13\}

Posted 3 months ago

Question

What interval does this inequality represent?

\newline

\newline

[A](-3,\infty)

\newline

[B](-3,\infty)

\newline

[C](-\infty,-3)

\newline

[D](-\infty,-3]

Posted 3 months ago

Question

Which of the following expressions is equivalent to

\newline

106 \times 3.7

\newline

1

\newline

106 \times 37 \div 10

\newline

106 \times 37 \div 100

\newline

106 \times 37 \div 1,000

\newline

106 \times 37 \div 10,000

Posted 4 months ago

Question

What is the value of

x^{6}+y^{2}

x=1

y=9

Posted 1 month ago

Question

What is the value of

y^{2}-x^{2}

x=5

y=6

Posted 2 months ago

Question

What is the value of

y^{2}-x^{4}

y=8

x=2

Posted 4 months ago

Question

A physicist measures the energies of atoms

A

B

to be the positive values

a

b

respectively. He determines that the energy of atom

B

is between one percent more than and one percent less than twice the energy of atom

A

. Which of the following systems of inequalities best models the possible range of values for the energies of atoms

A

B

\newline

1

\newline

\left\{\begin{array}{l}a<2.02 b \\ a>1.98 b\end{array}\right.

\newline

\left\{\begin{array}{l}a<2 b+0.02 \\ a>2 b-0.02\end{array}\right.

\newline

\left\{\begin{array}{l}b<2.02 a \\ b>1.98 a\end{array}\right.

\newline

\left\{\begin{array}{l}b<2 a+0.02 \\ b>2 a-0.02\end{array}\right.

Posted 2 months ago

Question

2+2(8347-4783)=-2 j

, then what is the value of

-j

Posted 17 days ago