Let $$a(x,y)$$, $$b(x,y)$$ and $$c(x,y)$$ be three statements with variables $$x$$ and $$y$$ chosen from some universe. Consider the following statement: $$$\left( {\exists x} \right)\left( {\forall y} \right)\left[ {\left( {a\left( {x,\,y} \right) \wedge b\left( {x,\,y} \right)} \right) \wedge \neg c\left( {x,\,y} \right)} \right]$$$

Which one of the following is its equivalent?

Identify the correct translation into logical notation of the following assertion.

$$Some\,boys\,in\,the\,class\,are\,taller\,than\,all\,the\,girls$$
Note: taller$$\left( {x,\,y} \right)$$ is true if $$x$$ is taller than $$y$$.

Consider a System with a two-level paging scheme in which a regular memory access takes $$150$$ nanoseconds, and servicing a page fault takes $$8$$ milliseconds. An average instruction takes $$100$$ nanoseconds of $$CPU$$ time, and two memory accesses. The $$TLB$$ hit ratio is $$90$$% and the page fault rate is one in every $$10,000$$ instructions. What is the effective average instruction execution time?

The minimum number of page frames that must be allocated to a running process in a virtual memory environment is determined by.