The mixing vat in a factory receives liquid ingredients through six separate valves-labeled R, S, T, U, Y and Z each of which has exactly two settings: Open and closed. The mixing vat operator must ensure that each valve is set open or closed according to the following conditions:
i. If T is open, both S and Z must be closed;
ii. R and Z cannot both be closed at the same time.
iii. If Y is closed, Z must also be closed;
iv. S and U cannot both be pen at the same time.
If the maximum number of valves that can be closed at the same time are closed, which of the following must be true?
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