1. **Stating the problem:** We want to analyze the inequality $$(a - \frac{1}{2})(b - \frac{1}{2}) \neq 0$$ which means the product of the two terms is not equal to zero. 2. **Formula and rules:** The product of two factors is zero if and only if at least one of the factors is zero. Therefore, for the product to be nonzero, neither factor can be zero. 3. **Intermediate work:** - Set each factor not equal to zero: $$a - \frac{1}{2} \neq 0 \implies a \neq \frac{1}{2}$$ $$b - \frac{1}{2} \neq 0 \implies b \neq \frac{1}{2}$$ 4. **Explanation:** This means that for the product to be nonzero, both $a$ and $b$ must be different from $\frac{1}{2}$. If either $a$ or $b$ equals $\frac{1}{2}$, the product becomes zero. **Final answer:** $$a \neq \frac{1}{2} \quad \text{and} \quad b \neq \frac{1}{2}$$