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}

Solution

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