Unless otherwise specified, assignments are due next class meeting Excrcise l Let: N New York is larger than Chicago W "New York is north of Washington' C 'Chicago is larger than New York (Thus N and W are true and C is false) Find the truth value of the following statements: a- Nv C Exercise 2: ranslate the following compound sentences into symbolic notation, using letters to stand for ion atomic sentences: Either the fire was produced by arson or it was produced by spontaneous combust a- if the water is clear, then either Henry can see the bottom of the pool or his eyes are closed. Either housing is scare or people like to live with their in-laws, and if people do not b- c- like to live with their in-laws then housing is scarce. d- Sophomore like physics only if they like mathematics(Sx, Px, Mx) need les Given any number x, there is a smaller number y (Nx, Sxy) f. For any 2 numbers x and y, the sum of x and y is the same as the sum of y and x Exercise 3: For the following argument, try to construct sentential derivations. In some cases, the argument is invalid, in which case write"CDNFconclusion does not follow), use the letter indicated: 1. If Algernon is in jail, then he is not a nuisance to his family. If he is not in jail, then he is not a disgrace. If he is not a disgrace, then he is in the army. Therefore he is in the army.(J, N, D. A) 2. If Algernon is a nuisance, then he is not in jail. If he is in jail, then he is a disgrace. If he is a disgrace, then he is not in the army. Therefore, he is either not in the army or not a nuisance(J,N,D,A). Some foolish people drink whiskey. Some students do not drink whiskey. Therefore some students are not foolish.(F(x), S(x), W(x)) 3. ne74. Seniors only date juniors. Sam is a Senior. Sam dates Julie. Therefore Julie is a variables junior.(S(x), Dix.y), J(x) Seniors who like mathematics do not date Elizabeth. Elizabeth only dates seniors. George dates Elizabeth. Therefore George does not like mathematics. 5. A) For the following arguments, give either a direct proof or an indirect proof of validity: Av B Some men are liars, John is a man Therefore John is a liar