Homework 7: Syntactic structurePhrase Structure Rules to use in Q2 and Q3. a. S → DP AuxP b. i. NP → AdjP NP ii. NP → NP PP iii. NP → N g. CP → C S c. i. VP → AdvP VP ii. VP → VP PP iii. VP → V (DP) (PP) (CP) h. AuxP → Aux VP d. PP → P DP c'. VP → BE AP j. DP → D (NP) e. AP → (AdvP) (Deg) A f. AdvP → (Deg) Adv NOTE: for names, mass nouns, and plurals, it's ok to have a silent Determiner, as in this tree:Lexicon (remember that you can add new words to existing categories freely)N → owl, table, ball, man, cookie, telescope, eggs, hams, candies, leaders, tomatoes, kittens, old, Sam, Brandeis... D → I, we, you, this, the, more, some, my, his, your, every, no …Adj → tall, nice, green, little, intelligent, old …P → on, from, with, in …Aux → should, might, can, be, doV → see, like, hit, be, need, tell, eat, help, kiss, grow, man, run, sleep, grow...Deg → more, very, so...Adv → slightly, suddenly, totally, ...Conj → and, or ...C → thatQuestion 1. Constituency tests In the lecture we discussed three tests for constituency (pro-form substitution test, movement test, stand-alone/question test). (a) Are the underlined word strings in the following sentences constituents? (answer yes or no)(b) Which tests are applicable for each? Provide the test sentences (whenever using the stand-alone test, give the question as well).1. Marge read the old newspaper.2. Marge read the old newspaper.3. Three silly white sheep dance.4. Three silly white sheep dance.5. The clouds roll across the sky.6. The thieves opened the door with a credit card.Question 2. Improving the theoryDraw a tree for the following sentence, according to the rules above. Make sure to label every node.1. My intelligent students from Intro can tell you that syntax is very easy in no time.Now, consider the following sentences:2. Intelligent and eloquent students from Intro may talk about this.3. My students and advisees can and do solve phonology problems. 4. My students and their TAs like Turkish morphology.5. Each and every student can tell you that syntax is easy and semantics is fun.6. *My and intelligent students like the class.7. *Sophia can dance the tango and in the woods.8. *We did our homework and see this. (Intended meaning: We did our homework and we did see this)A. What is structurally (syntactically) different about sentences (2-5) compared to (1)? Make sure you discuss the constituency of sentences (2-5) (remember to try constituency tests!)1B. What changes to the rules in a-f above (tree-building rules) are needed to account for sentences (2-5)? Propose a new rule or rules (HINT: you won't need to add new part-of-speech categories to the lexicon, since I already provide one for and). (NB: make sure your rule system STILL accounts for (1) also!)C. Draw trees for 2 of the grammatical sentences above (your choice which ones).D. Explain exactly what causes the ungrammaticality in (6-8) in your system. Question 3. Structural ambiguity All but one of the following sentences has a structural ambiguity.1. Sam likes green eggs and ham.2. I ate red candies and a cookie.3. We need more intelligent leaders.A. Provide complete labeled tree diagrams for both interpretations of each ambiguous sentence (that's four trees total) – use the phrase structure rules in the beginning of HW and additional one(s) from Question 2!B. Identify by paraphrasing which interpretation corresponds to which structure. Make sure that your paraphrases are not ambiguous! C. For the sentence that is not ambiguous, draw the one appropriate tree, and explain what rules out interpretation as a different structure, using trees and rules to