From the uploaded image, I see a mathematical task related to sets $A$ and $B$, where the problem is to find and represent $A \cup B$, $A \cap B$, and $A \setminus B$ on the number line. The sets $A$ and $B$ are defined as:

$A = \{x \in \mathbb{R} \mid x^2 - 1 \leq 0\},$ $B = \{x \in \mathbb{R} \mid \frac{5}{6} \leq x \leq \frac{7}{2}\}.$

Step-by-step Solution:

1. Analyze Set $A$:

The inequality $x^2 - 1 \leq 0$ can be rewritten as: $x^2 \leq 1 \quad \text{or} \quad -1 \leq x \leq 1.$ Thus, $A = [-1, 1]$.

2. Analyze Set $B$:

The inequality $\frac{5}{6} \leq x \leq \frac{7}{2}$ describes an interval: $B = \left[\frac{5}{6}, \frac{7}{2}\right].$

3. Operations Between Sets:

• Union ($A \cup B$): The union combines all elements from $A$ and $B$: [ A \cup B = [-1, 1] \cup \left[\frac{5}{6}, \frac{7}{2}\right]. ] Simplify the union: Since ( \frac{5}{6} \