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Valuation functions of observables in quantum mechanics are often expected to obey two constraints called the sum rule and product rule. However, the Kochen-Specker (KS) theorem shows that for a Hilbert space of quantum mechanics of dimension d ≥ 3, these constraints contradict individually with the assumption of value definiteness.The two rules are not irrelated and Peres [Found. Phys. 26 (1996)807] has conceived a method of converting the product rule into a sum rule for the case of two qubits. Here we apply this method to a proof provided by Mermin based on the product rule for a three-qubit system involving nine operators. We provide the conversion of this proof to one based on sum rule involving ten operators.