1. The problem defines two sets: - Set A: $A = \{x \in \mathbb{R} : |x| < 1/2\}$, which means all real numbers $x$ whose absolute value is less than $1/2$. - Set B: $B = \{x \in \mathbb{R} : |x| \geq 1/2\}$, which means all real numbers $x$ whose absolute value is greater than or equal to $1/2$. 2. To understand these sets, recall that $|x|$ represents the distance of $x$ from zero on the number line. 3. For set A, $|x| < 1/2$ means $x$ lies strictly between $-1/2$ and $1/2$: $$-\frac{1}{2} < x < \frac{1}{2}$$ 4. For set B, $|x| \geq 1/2$ means $x$ lies outside or on the boundaries of the interval $[-1/2, 1/2]$: $$x \leq -\frac{1}{2} \quad \text{or} \quad x \geq \frac{1}{2}$$ 5. These two sets partition the real numbers into two disjoint parts: numbers inside the open interval $(-1/2, 1/2)$ and numbers outside or on the boundary of this interval. Final answer: - $A = \{x \in \mathbb{R} : -\frac{1}{2} < x < \frac{1}{2}\}$ - $B = \{x \in \mathbb{R} : x \leq -\frac{1}{2} \text{ or } x \geq \frac{1}{2}\}$