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Which is the set of integers greater than or equal to $0$ and less than or equal to $6$ ? $\newline$ Choices: $\newline$ (A) $\{1, 2, 3, 4, 5, 6\}$ $\newline$ (B) $\{1, 6\}$ $\newline$ (C) $\{0, 1, 2, 3, 4, 5, 6\}$ $\newline$ (D) $\emptyset$

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Set-builder notation

Full solution

Q. Which is the set of integers greater than or equal to

0

and less than or equal to

6

?

\newline

Choices:

\newline

(A)

\{1, 2, 3, 4, 5, 6\}

\newline

(B)

\{1, 6\}

\newline

(C)

\{0, 1, 2, 3, 4, 5, 6\}

\newline

(D)

\emptyset

Understand the problem: Understand the problem. $\newline$ We need to find the set of integers that are greater than or equal to $0$ and less than or equal to $6$ .
Identify the inequality signs: Identify the inequality signs. $\newline$ The problem asks for numbers greater than or equal to $0$ and less than or equal to $6$ . The inequality signs for these conditions are $\geq$ and $\leq$ respectively.
Determine the set of integers: Determine the set of integers that satisfy both conditions. $\newline$ We need to list the integers that are both greater than or equal to $0$ and less than or equal to $6$ . This includes all whole numbers starting from $0$ up to and including $6$ .
Write down the set of integers: Write down the set of integers that satisfy the conditions. $\newline$ The set of integers is $\{0, 1, 2, 3, 4, 5, 6\}$ .
Match the set with choices: Match the set with the given choices. $\newline$ The correct set that matches our result is $(C)\{0, 1, 2, 3, 4, 5, 6\}$ .

More problems from Set-builder notation

Question

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

S = \{2, 12\}

R \cup S

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Which is the set of integers greater than or equal to

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

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A physicist measures the energies of atoms

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

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B

\newline

1

\newline

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

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

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