Question $2[30$ marks$]$

$($a$)$ Define Problem Management and distinguish it from Incident Management. Explain why Problem Management is crucial for ensuring the stability and reliability of IT services. $[10$ marks$]$

$($b$)$ Discuss the Problem Management lifecycle, including identification, investigation, resolution, and closure of problems. Explain how proactive Problem Management differs from reactive Problem Management. $[10$ marks$]$

$($c$)$ Explore the relationship between Incident Management and Problem Management. How do these processes complement each other in maintaining IT service quality? Provide examples to support your explanation.