CSCE 625 - HW5due: Wed, Oct 261. Translate the following sentence into first-order logic (use underlined symbols as simple predicates):- A poodle is a small, fluffy dog.- Someone from the post-office is at the front door of John’s house.- Tomatos are either a fruit or vegetable.- Beef is a type of meat, rather than fruit or vegetable.- All Romans were either loyal to Ceasar or hated him.- People only TryToAssassinate rulers they are not loyal to.2. Using Intervals and Events, translate the following into first-order logic.- If it is rainy, then drivers ShouldStop at yellow lights.- Nobody can light a fire when it is raining.- A firecracker will go off (explode) between 10 and 20 seconds after you light the fuse, unless it is a “dud”.- There is always sunshine when the wind comes from the East.- When it is cold and foggy, Doug’s neighbor practices the flute.- Doug’s neighbor never practices an instrument for more than an hour.- When it is cold and Doug feels rheumatic, Doug lights a fire in his fireplace.- Lighting a fire built from wet wood causes smoke.- When Doug’s fire smokes, he opens the door or window.3. Translate the following sentences into first-order logic:- Al and Bob are brothers.- They both bought computers from the same manufacturer.- Al bought his computer a year before Bob.- Bob’s computer crashed, then he got it repaired at Best Buy for $100.4. Describe a model for the following set of sentences:{-friend(a,b), -x-y friend(x,y), -x-y friend(x,y)-friend(y,x)}5. You are the proprietor of Sammy’s Sport Shop. You have just received a shipment of three boxes filled with tennis balls. One box contains only yellow tennis balls, one box contains only white tennis balls, and one contains both yellow and white tennis balls. Youwould like to stock the tennis balls in appropriate places on your shelves. Unfortunately, the boxes have been labeled incorrectly; the manufacturer tells you that you have exactly one box of each, but that each box is definitely labeled wrong.a) Write down a set of sentences in first-order logic that captures all the relevant information about the problem (such as what observing a white ball drawn from box 2 implies, that at most one box can contain yellow balls, etc.).b) Use natural deduction (first-order rules of inference) to prove that box 2 contains whitetennis