Phil HOMEWORK #4 Due Monday, October 4 at the beginning of class. Late homework will not be accepted.
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1 Phil HOMEWORK #4 Due Monday, October 4 at the beginning of class. Late homework will not be accepted. In each of the following, you may use either the full paraphrase (e.g. ( x)(x is fat) ) or a paraphrase using monadic predicate letters (e.g. ( x)(fx) ), provided in the latter case that you specify predicate letter assignment. 1. Paraphrase the following, using the existential quantifier: (a) Chubby narwhals exist. (i) ( x)(x is chubby x is a narwhal) (ii) ( x)(cx Nx) C : is chubby N : is a narwhal (b) Some people are cold are some are warm. (i) ( x)(x is a person x is cold) ( x)(x is a person x is warm) (ii) ( x)(px Cx) ( x)(px Wx) C : is cold W : is warm (c) One of Batman s villains dresses like a clown. (i) ( x)(x is one of Batman s villains x dresses like a clown) (ii) ( x)(bx Cx) B : is one of Batman s villains C : dresses like a clown (d) There is a crazed gunman on campus. (i) ( x)(x is a crazed x is a gunman x is on campus) (ii) ( x)(cx Gx Ox) C : is crazed G : is a gunman O : is on campus (e) There are some exam questions that are neither essays nor multiple choice. (i) ( x)(x is an exam question (x is an essay) (x is multiple choice)) (ii) ( x)(qx Ex Mx) Q : is an exam question E : is an essay M : is multiple choice (f) If there is a way out, then there isn t a reason to panic. (i) ( x)(x is a way out) ( x)(x is a reason to panic) (ii) ( x)(wx) ( x)(rx) W : is a way out R : is a reason to panic 1
2 2. Paraphrase the following, using the universal quantifier: (a) Everything is going to be OK. (i) ( x)(x is going to be OK) (ii) ( x)(gx) G : is going to be OK (b) Every horse in the room is a stallion. (i) ( x)(x is a horse x is in the room x is a stallion) (ii) ( x)(hx Rx Sx) H : is a horse R : is in the room S : is a stallion (c) Pictures are worth 1000 words. (i) ( x)(x is a picture x is worth 1000 words) (ii) ( x)(px Wx) P : is a picture W : is worth 1000 words (d) Only tall men can play basketball. (i) ( x)(x plays basketball x is tall x is a man) (ii) ( x)(bx Tx Mx) B : plays basketball T : is tall M : is a man (e) Any student who doesn t study won t pass the exam. (i) ( x)(x is a student (x studies) (x will pass the exam)) (ii) ( x)(sx Fx Px) F : studies P : will pass the exam (f) No politician elected to office is both a Democrat and a Republican. (i) ( x)(x is a politician x is elected to office (x is a Democrat) v (x is a Republican)) or ( x)(x is a politician x is elected to office (x is a Democrat x is a Republican)) (ii) ( x)(px Ex Dx v Rx) or ( x)(px Ex (Dx Rx)) P : is a politician E : is elected to office D : is a Democrat R : is a Republican 2
3 3. Paraphrase each of the following twice, once as an existential quantification, and once as a universal quantification. (a) No student who fails logic will be a philosopher. (i) ( x)(x is a student x fails logic x will be a philosopher) (ii) ( x)(sx Fx Px) P : will be a philosopher (i) ( x)(x is a student x fails logic (x will be a philosopher)) (ii) ( x)(sx Fx Px) P : will be a philosopher (b) No student will both fail logic and become a philosopher. (i) ( x)(x is a student x will fail logic (i) ( x)(x is a student (x will fail logic x will become a philosopher) x will become a philosopher)) (ii) ( x)(sx Fx Px) (ii) ( x)(sx (Fx Px) S : : is a student F : will fail logic F : will fail logic P : will become a philosopher P : will become a philosopher (c) No one who fails logic is a student who will become a philosopher. (i) ( x)(x fails logic x is a student x (i) ( x)(x fails logic (x is a student x will become a philosopher)) will become a philosopher)) (ii) ( x)(fx Sx Px) (ii) ( x)(fx (Sx Px)) P : will become a philosopher P : will become a philosopher 4. Paraphrase the following into quantificational notation: (a) All dogs are boys and all cats are girls. (i) ( x)(x is a dog x is a boy) ( x)(x is a cat x is a girl) (ii) ( x)(dx Bx) ( x)(cx Gx) D : is a dog B : is a boy C : is a cat G : is a girl (b) If anyone knows a way out, then every cloud has a silver lining. (i) ( x)(x knows the way out) ( x)(x is a cloud x has a silver lining) (ii) ( x)(kx) ( x)(cx Sx) K : knows the way out C : is a cloud S : has a silver lining 3
4 (c) Only persons over 5'2" who are at least 12 years of age may ride the rollercoaster. (i) ( x)(x is riding the rollercoaster x is a person x is over 5'2" x is at least 12 years of age) (ii) ( x)(rx Px Ox Ax) R : is riding the rollercoaster O : is over 5'2" A : is at least 12 years of age (d) Canadian citizens were either born in Canada or were naturalized. (i) ( x)(x is a Canadian citizen x was born in Canada v x was naturalized) (ii) ( x)(cx Bx v Nx) C : is a Canadian citizen B : was born in Canada N : was naturalized (e) Every Keanu Reeves movie is excellent only if not every Keanu Reeves movie has been released. (i) ( x)(x is a Keanu Reeves movie x is excellent) ( x)(x is a Keanu Reeves movie x has been released) or ( x)(x is a Keanu Reeves movie x is excellent) ( x)(x is a Keanu Reeves movie (x has been released)) (ii) ( x)(kx Ex) ( x)(kx Rx) or ( x)(kx Ex) ( x)(kx Rx) K : is a Keanu Reeves movie E : is excellent R : has been released (f) If everything is going to be OK, then there isn t a reason to panic. (i) ( x)(x is going to be OK) ( x)(x is a reason to panic) (ii) ( x)(ox) ( x)(rx) O : is going to be OK R : is a reason to panic (g) Boys are smelly and girls are made of rainbows. (i) ( x)((x is a boy x is smelly) (x is a girl x is made of rainbows)) or ( x)(x is a boy x is smelly) ( x)(x is a girl x is made of rainbows) (ii) ( x)((bx Sx) (Gx Rx)) or ( x)(bx Sx) ( x)(gx Rx) B : is a boy S : is smelly G : is a girl R : is made of rainbows 4
5 (h) Puppies and kittens don t like Old Man Winter. (i) ( x)(x is a puppy v x is a kitten (x likes Old Man Winter)) or ( x)(x is a puppy (x likes Old Man Winter)) (x is a kitten (x likes Old Man Winter)) or ( x) (x is a puppy (x likes Old Man Winter)) ( x) (x is a kitten (x likes Old Man Winter)) (ii) ( x)(px v Kx (Ox)) or ( x)(px (Ox)) (Kx (Ox)) or ( x)(px (Ox)) ( x)(kx (Ox)) B : is a puppy S : is a kitten G : likes Old Man Winter (i) If any Canadian farmer moves to Texas, then s/he will be accepted. (i) ( x)(x is Canadian x is a farmer x moves to Texas x will be accepted) (ii) ( x)(cx Fx Mx Ax) C : is Canadian F : is a farmer M : moves to Texas A : will be accepted (j) If there isn t a way out, then all the townsfolk are doomed. (i) ( x)(x is a way out) ( x)(x is a townsperson x is doomed) (ii) ( x)(ox) ( x)(tx Dx) C : is a way out F : is a townsperson M : is doomed (k) Considerate men don t exist. (i) ( x)(x is a man x is considerate) or ( x)(x is a man (x is considerate) or ( x)(x is considerate (x is a man)) (ii) ( x)(mx Cx) or ( x)(mx Cx) or ( x)(cx Mx) M : is a man C : is considerate (l) Andrew likes any person whom Bart does not like. (i) ( x)(x is a person (Bart likes x) (Andrew likes x) (ii) ( x)(px (Bx) (Ax) B : Bart likes A : Andrew likes NOTE: Your answers should be handwritten. Make certain your name and section number (70X) are on your submitted homework. 5
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