Consider the SQL Query given below.

$10$ marks

SELECT Passenger. ticketno FROM Train, Passenger, Inspector WHERE Train. tno$=$Inspector.no AND Train.Date$=\text{'}05-07-2023\text{'}$ AND Train.to$=$ Chennai' AND Passenger.name$=$Inspector.name

a$.$ Convert the following query into relational algebra expressions. $3$ marks

b$.$ Reduce the relational algebra expression to an equivalent expression by applying the equivalence rules $3$ marks

c$.$ Draw query trees for the two relational algebra expressions. $3$ marks

d$.$ State which tree is better in terms of cost of the query execution and why? $1$ mark