Which type of firewall is specifically designed to monitor and filter incoming and outgoing traffic based on predetermined security rules and is capable of inspecting the state of network connections? 

A Stateful Firewall is specifically designed to monitor and filter traffic based on the state of active connections. Unlike stateless firewalls, which only consider individual packets, stateful firewalls keep track of the state of network connections, allowing them to determine whether a packet is part of an existing connection or if it is a new connection request. This ability to inspect the entire context of network traffic enables stateful firewalls to apply more sophisticated security policies and make more informed decisions regarding packet filtering, thus providing better protection against unauthorized access and attacks. Why Other Options are Incorrect: A) Stateless Firewall: Stateless firewalls do not track the state of connections and make filtering decisions based solely on predefined rules, which is less secure than stateful inspection. B) Application Firewall: Application firewalls focus on filtering traffic at the application layer, specifically monitoring and filtering HTTP or other application-specific protocols, rather than tracking connection states. C) Packet-Filtering Firewall: Packet-filtering firewalls examine individual packets against predefined rules but do not maintain information about the state of connections. E) Proxy Firewall: Proxy firewalls act as intermediaries between clients and servers, filtering requests and responses but do not track connection states like stateful firewalls.