A non-planar graph with minimum number of vertices has

Uses Modus ponens $$\left( {A,\,\,A \to B\,|\,\, = B} \right)$$ or resolution to show that the following set is inconsistent:

(1) $$Q\left( x \right) \to P\left( x \right)V \sim R\left( a \right)$$
(2) $$R\left( a \right) \vee \sim Q\left( a \right)$$
(3) $$Q\left( a \right)$$
(4) $$ \sim P\left( y \right)$$
where $$x$$ and $$y$$ are universally quantifies variables, $$a$$ is a constant and $$P, Q, R$$ are monadic predicates.

A computer system has 6 tape drives, with n process completing for them. Each process may need 3 tape drives. The maximum value of n for which the system is guaranteed to be deadlock free is:

Let the page reference and the working set window be c c d b c e c e a d and 4, respectively. The initial working set at time $$t = 0$$ contains the pages {a, d, e}, where a was referenced at time $$t = 0, d$$ was referenced at time $$t = -1,$$ and $$e$$ was referenced at time $$t = -2.$$ Determine the total number of page faults and the average number of page frames used by computing the working set at each reference.