B.5.QD.CF:5.1 - Distinguish operating conditions without inventing a machine

A proposed device has one fixed setting p. The task requires p to be at least 6 during work and at most 2 during quiet operation. In the proposed design, both requirements constrain the same fixed value; no such value exists.

Recover the extra premise: the setting is fixed across those operating conditions. Let p_work and p_quiet describe the two values. The account is:

• p_work ≥ 6;
• p_quiet ≤ 2;
• p_work = p_quiet.

Keeping the two requirements and reconsidering the equality produces a construction question: Can the device select different settings in the two distinguishable conditions? The values (6,2) satisfy the revised inequalities. They identify what a switching construction would have to supply.

That answer is conditional. The device must be able to recognize the condition and reach the required setting in time, using the resources permitted by the task. If a transition takes three seconds while the retained requirement allows one second, this proposed transition fails. A faster operation, another construction or an authorized requirement change is still needed.

If instead both inequalities concern the same operation at the same time, separating their names would misrepresent the task. The inequality 6 ≤ p ≤ 2 remains impossible. The useful result then identifies the requirements that cannot both be retained.