$($a$)$ Describe the opening of a TCP connection $($giving the state transition diagram$)$ and indicate the role played by various TCP header fields in this process.$($b$)$ Describe the closing of a TCP connection $($giving the state transition diagram$)$ and indicate the role played by various TCP header fields in this process.$($c$)$ Relate the socket APIs to the steps involved in opening and closing a TCP connection. $($d$)$ Explain the working of the slow start mechanism for congestion control$-$ is it really slow $($illustrate with a diagram$)?($e$)$ What is fast retransmit in the context of congestion control and how does it work $($illustrate with a diagram$)?$