Please need help! Use the table names as an example to help better answer the questions. Use Tarski World Program to understand the questions better.

homework #7A Write up 12.14 (p. 344); 12.23 (p. 346). Also, as part of your assigned homework, translate the following into FOL, and then present an informal proof of it: \"All the world loves a lover. Someone loves someone. Therefore, everyone loves everyone.\" Hint: Translate \"All the world loves a lover\" as: AxAy[EzLoves(y,z) --> Loves(x,y)] (The version of that FOL sentence in the syllabus has a stray parenthesis, actually. Sorry about that!) Finally, as part of your assignment, explain in a few sentences either (i) why that's a good translation into FOL, or, (ii) if you think it is not actually a good translation, why it is not. Exercises The following essercises each contain a formal argument and something that purports to be an informal proof of it. Some of these proofs are correct while others are not. Give a logical critique of the purported proof. Your critique should take the form of a short essay that makes explicit each proof step or method of proof used, indicating whether it is valid or not. If there is a mistake, see if can you patch it up by giving a correct proof of the conclusion from the premises. If the argument in question is valid, you should be able to fla' up the proof. If the argument is invalid, then of course you will not be able to fix the proof. The following exercises each contains an argument; some are valid, some not. If the argument is valid, give an informal proof. If it is not valid, use Tarski's World to construct a counterexample. 12.4 Vy [Cube(y) V Dodec(y)] 12.5 [(apoa / ( Large(x)] Vx [Cube(x) -+ Large(x)] 3x -Large(x) 3x -Large(x) Ex Dodec(x) 3x [Dodec(x) A Small(x)]Table 1.2: Names and predicates for a language. ENGLISH FOL COMMENT Names: Max max Claire claire Folly folly The name of a certain dog. Carl carl The name of another dog. Scruffy scruffy The name of a certain cat. Pris pris The name of another cat. 2 pm, Jan 2, 2011 2:00 The name of a time. 2:01 pm, Jan 2, 2011 2:01 One minute later. . . . . . . Similarly for other times. Predicates: x is a pet Pet (x) x is a person Person (x) x is a student Student(x) t is earlier than t' t