1. **State the problem:** We want to determine if the inequality $\frac{1}{2} \geq \frac{e}{2}$ is true. 2. **Recall the inequality rule:** When both sides of an inequality are divided by the same positive number, the inequality direction remains the same. 3. **Simplify the inequality:** Multiply both sides by 2 (which is positive) to eliminate the denominators: $$\frac{1}{2} \geq \frac{e}{2} \implies 1 \geq e$$ 4. **Evaluate the constants:** The number $e$ (Euler's number) is approximately $2.718$, which is greater than 1. 5. **Compare values:** Since $1$ is not greater than or equal to $2.718$, the inequality $1 \geq e$ is false. 6. **Conclusion:** Therefore, the original inequality $\frac{1}{2} \geq \frac{e}{2}$ is false.