Let $$S$$ be an infinite set and $${S_1},\,\,{S_2},....\,\,{S_n}$$ be sets such that $${S_1} \cup {S_2} \cup ....... \cup {S_n} = S$$. Then

Show that proposition $$C$$ is a logical consequence of the formula $$A \wedge \left( {A \to \left( {B \vee C} \right) \wedge \left( {B \to \sim A} \right)} \right)$$ using truth tables.

Assume that the following jobs are to be executed on a single processor system.

Job Id	CPU Burst Time
p	4
q	1
r	8
s	1
t	2

The jobs are assumed to have arrived at time $${0^ + }$$ and in the order $$p,q,r,s,t.$$ Calculate the departure time (completion time) for job $$p$$ if scheduling is round robin with time slice$$1.$$

Consider a system having m resources of the same type. These resources are shared by 3 processes A, B and C, which have peak demands of 3, 4 and 6 respectively. For what value of m deadlock will not occur?