Let $$P, Q$$ and $$R$$ be three atomic prepositional assertions. Let $$X$$ denotes $$\left( {P \vee Q} \right) \to R$$ and $$Y$$ denote $$\left( {P \to R} \right) \vee \left( {Q \to R} \right)$$.

Which one of the following is a tautology?

What is the swap space in the disk used for?

Suppose n processes, P₁,......., P_n share m identical resource units, which can be reserved and released one at a time. The maximum resource requirement of process P_i is S_i, where S_i > 0. Which one of the following is a sufficient condition for ensuring that deadlock does not occur?

Consider a disk drive with the following specifications:
$$16$$ surfaces, $$512$$ tracks/surface, $$512$$ sectors/track, $$1$$KB/Sector, rotation speed $$3000$$ rpm. The disk is operated in cycle stealing mode whereby whenever one $$4$$ byte word is ready it it's sent to memory; similarly, for writing, the disk interface reads a $$4$$ byte word from the memory in each $$DMA$$ cycle Memory cycle time is $$40$$nsec. The maximum percentage of time that the $$CPU$$ gets blocked during $$DMA$$ operation is: