Questions: Decide if each set is written in interval notation or in set-builder notation. - (-∞, 5] ∪ (6, ∞) Select an answer ✓ - x -3 ≤ x ≥ 0 Select an answer Y - x x ≠ 1 Select an answer ✓ - (7,3) Select an answer ✓ - [0,5) Select an answer ✓ Question Help: Video - set builder notation - interval notation

Decide if each set is written in interval notation or in set-builder notation.

- (-∞, 5] ∪ (6, ∞) Select an answer ✓
- x  -3 ≤ x ≥ 0 Select an answer Y
- x  x ≠ 1 Select an answer ✓
- (7,3) Select an answer ✓
- [0,5) Select an answer ✓

Question Help: Video
- set builder notation
- interval notation
Transcript text: Decide if each set is written in interval notation or in set-builder notation. \begin{tabular}{|c|c|} \hline$(-\infty, 5] \cup(6, \infty)$ & Select an answer $\checkmark$ \\ \hline$\{x \mid-3 \leq x \geq 0\}$ & Select an answer $Y$ \\ \hline$\{x \mid x \neq 1\}$ & Select an answer $\checkmark$ \\ \hline$(7,3)$ & Select an answer $\checkmark$ \\ \hline$[0,5)$ & Select an answer $\checkmark$ \\ \hline Question Help: Video & \begin{tabular}{l} set builder notation \\ interval notation \end{tabular} \\ \hline \end{tabular}
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Solution

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Solution Steps

To determine if each set is written in interval notation or set-builder notation, we need to understand the differences between the two. Interval notation uses brackets and parentheses to describe a range of values, while set-builder notation uses a description or condition to define a set. We will check each set and classify it accordingly.

Step 1: Identify Notation Types

To determine the type of notation used for each set, we need to recognize the characteristics of interval and set-builder notation. Interval notation uses parentheses (( and brackets [[ to denote ranges, while set-builder notation uses curly braces {\{ and a condition or rule to define the set.

Step 2: Classify Each Set
  • Set 1: (,5](6,)(-∞, 5] ∪ (6, ∞) uses parentheses and brackets, indicating it is in interval notation.
  • Set 2: {x3x0}\{x \mid -3 \leq x \geq 0\} uses curly braces and a condition, indicating it is in set-builder notation.
  • Set 3: {xx1}\{x \mid x \neq 1\} also uses curly braces and a condition, indicating it is in set-builder notation.
  • Set 4: (7,3)(7,3) uses parentheses, indicating it is in interval notation. However, note that this interval is not valid as it implies an empty set.
  • Set 5: [0,5)[0,5) uses brackets and parentheses, indicating it is in interval notation.

Final Answer

(,5](6,)(-∞, 5] ∪ (6, ∞): Interval notation

{x3x0}\{x \mid -3 \leq x \geq 0\}: Set-builder notation

{xx1}\{x \mid x \neq 1\}: Set-builder notation

(7,3)(7,3): Interval notation (invalid, empty set)

[0,5)[0,5): Interval notation

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