question is provided on the course website. $2.|8$ marks$|$ In this question, you are asked to model connections between actors using predicate logic. Let D be the domain of every actor, alive or dead, who has ever been in any movie. Let C be the co$-$star predicate on pairs of actors from D$,$ defined by C$($x$.$ y$)=$ x andy have been in a movie together.$\text{'}$ The 'Bacon game' is a game where players try to connect individuals to the actor Kevin Bacon by using the co$-$star predicate C$.$ The Bacon number of an actor x $($that is$,$ where x is an element of D$)$ is the smallest number of links needed, using the co$-$star predicate C$,$ to connect x to Kevin Bacon. For example, Daniel Kaluuya was in the movie Sicario with Jeffrey Donovan, who in turn was in Sleepers with Kevin Bacon. So$,$ Daniel Kaluuya has a Bacon number of $2.($This example was generated by oracleofbacon.org, where you can determine the Bacon number for many other actors.$)$ Let U$,$ D be Kevin Bacon, i$.$e$.,$ let bo be the special name that we give to Kevin Bacon, given the unique nature of his role in the game. a$.$ Write a predicate B$2($x$)$ in one variable that reflects that the Bacon number of an actor x $$ D is at most two. By the definition of the Bacon number, this means that there is some actor y such that x and y were in a movie together and that y and b$,$ were in a movie together. The expression for the predicate must involve a quantifier. b$.$ Similarly, write a predicate ba $($x$)$ in one variable that reflects that the Bacon number of an actor x is at most three. This will likely involve multiple quantifiers. c$.$ Notice for B$,($x$),$ the predicate reflects that the Bacon number of x is at most $3.$ The predicate does not enforce that the Bacon number is exactly $3,$ since there is a possibility that the actor x is$,$ e$.$g$.,$ in a movie with bo$,$ or has a Bacon number of $2$ through some other links. Write a predicate for an actor x E D to have Bacon number exactly three, called B$.($x$),$ by excluding these other possibilities. This predicate should be defined by using C$,$ Ba and Ba$.$ Be sure to exclude the possibility that x is Kevin Bacon. d$.$ Write a full expression for Ba $($x$)$ that does not use Ba or Ba$,$ but still uses C$.$ Make sure to parenthesize appropriately. $($Hint: use your solution for part c$.$ and negate as necessary$-)$ Write a short $(1-2$ sentence$)$ explanation of the entire predicate definition in natural language, verifying that it makes sense. this is discrete math predicate logic