Philosophy logic

1. Paraphrase the following, using the existential quantifier:

(a) Warm-blooded reptiles exist.

(b) There’s a man in the room with a bad cold.

(c) There are politicians who are clever but neither honest nor compassionate.

(d) Some clever logicians are not wise, but some are.

2. Paraphrase the following, using the universal quantifier:

(a) All prime numbers that are greater than two are odd.

(b) All of the witnesses who hold stock in the firm are employees who can keep a secret.

(c) Only mammals suckle their young.

(d) None but the strong can survive the epidemic.

(e) All students who are wise are clever.

(f) All students are both wise and clever.

3. Paraphrase each of the following twice, once as a negated existential quantification, and once as a universal quantification:

(a) No professor who is wise is clever.

(b) No professor is both wise and clever.

(c) No professor is either wise or clever.

4. Paraphrase the following into monadic quantificational notation:

(a) If all applicants of the class of ’69 received the second announcement, then some applicants not of the class of ’69 did not receive the second announcement.

(b) Some who take logic and Latin take neither physics nor Greek, but all who take either Latin or chemistry take both logic and Greek.

(c) A non-extinct animal is warm-blooded if and only if it is either a mammal or a bird.

(d) If something is neither ductile nor malleable, then not everything flexible is ductile.

(e) If something is neither ductile nor malleable, then it is not flexible.

(f) Only something which is either ductile or malleable is flexible.

(g) A dog will be happy provided that it is fed and petted.

(h) A patient will deteriorate if s/he gets bad care.

(i) A patient will deteriorate if and only if s/he gets bad care.

(j) Only men over 6′ tall and weighing more than 180 lbs. join the horse guard.

(k) Malone hates all New Yorkers, Bostonians, and Washingtonians.

(l) Dogs and children upset Mr. Fields.

5. Paraphrase the following into monadic quantificational notation:

(a) John likes somebody who respects Mary.

(b) John likes anybody who respects Mary.

(c) John does not like anybody who respects Mary.

(d) John does not respect anybody.

(e) John does not respect everybody.

(f) John likes any person whom Mary does not respect.

(g) John respects only those persons whom Mary likes.

(h) John respects no one whom Mary likes.

(i) Mary does not eat anchovies.

(j) Mary eats nothing but anchovies.