Explanation: (A) Condition 1: When x is divided by y, the remainder is z. By definition of remainder, \(z\) must be less than the divisor \(y\), so \(z < y\). Condition 2: When x is divided by z, the remainder is \((y-2)\). The remainder \((y-2)\) must be less than the divisor \(z\), so \(y-2 < z \implies y < z + 2\). Combining the inequalities: \(z < y < z + 2\). Since x, y, and z are positive integers, the only integer value for y between z and z+2 is \(y = z + 1\). Therefore, \(z = y - 1\) must be true.
