Question

14. Using the nouns N = {dog, man, mouse, bird) and the verbs V = {bites, eats, kicks}, how many "sentences" of the form " <noun > < verb > < noun > "are there, with the restriction that every word in the sentence has a different length? (For example, "dog eats mouse" is such a sentence, but "man bites dog" is not, because it contains two words of length three.) Use decision tree(s) to justify your answer. [5 points)

Answer 1

Solution: Giver that: SANDIM consider the following provided nocer and verb set vepre senled by N and v N = { dog, man, mouse, bird} V = { bites, eats, Kicks ] sen- If there is no restriction to form co tence, then it is possible to form 443x4 =48 Sentence Note that there are three decisions : 1. Choose roun as the first word of sentence noun may be dog or man or mouse or bird. The second word must be a verb but the length of verb must be different from first word noun 3. The third Word again must be a noen but the length Of noun must be different from first word noun and second word verb.

Therefore, every different length word in the sentence пCena has be formi The decision tree for sentences that can as Cnoun ) (verb) Crown) which are Selected from the noun and verb sets with the restriction that every word in the sente- a different length is as shown below. nce has bird dog els mouse marr go! ricks kicks eats bites eats kicks bites bites eals PO pran man dog man bird dog dog bird bird mouse bird house brid 0 2 0 0 0 המורדאן bird brood moye dog Une leals bite, kicks kicks bites eals brkicks bites eats mani dog man man bird dog dog mouse bird bird bird house

There bore, the total number of the serilence that can be form as Cnoun) Cverb) (noun) Which are selected from the houn and verb and verbor sets with the restriction that every word in the sentence has a different length is 12.