Let $$S = \left\{ {0,1,2,3,4,5,6,7} \right\}$$ and $$ \otimes $$ denote multiplication modulo $$8$$, that is, $$x \otimes y = \left( {xy} \right)$$ mod $$8$$

(a) Prove that $$\left( {0,\,1,\, \otimes } \right)$$ is not a group.
(b) Write $$3$$ distinct groups $$\left( {G,\,\, \otimes } \right)$$ where $$G \subset s$$ and $$G$$ has $$2$$ $$\,\,\,\,\,\,$$elements.

Let m[0] ..m[4] be mutexes (binary semaphores) and P[0] ...P[4] be processes. Suppose each process P[i] executes the following:

wait (m[i]); wait (m(m[(i+1) mod 4]))0;
.......
release (m[i]); release (m[(i+1) mod 4]);

This could cause

Suppose the time to service a page fault is on the average $$10$$ milliseconds, while a memory access takes $$1$$ microsecond. Then a $$99.99$$% hit ratio results in average memory access time of.

Which of the following is NOT a valid deadlock prevention scheme?