Math 180 Exercises - Kutztown University of Pennsylvania



Math 180 Exercise Set III, McLoughlin Fall 2001

1. Translate the following into symbolic form (do not forget to define symbols representing prime statements):

A. If this is Tuesday, we must be in Belgium.

B. It is a bird, if it is an eagle.

C. All people have heads.

D. She has no cash or she has a charge plate.

E. p2 ( 25, p = 5, or p = -5.

F. | y + 6 | ( 8 and y = 2 or y = -14.

G. If x + 3 = 5, then x = 1 or x = 2.

H. If z = 1 and z = 5, then z2 + 2z + 1 = 0.

I. It is snowing implies it is below 32( F.

J. It is not snowing or it is below 32( F.

K. It is necessary that x < 2 for x + 1 < 3.

L. If the Mets win every game left in the season, then they will win the N. L. East.

M. Tom always buys an Oldsmobile.

N. Sarah buys a Toy when she is in New York.

O. No chicken are teetotalers.

P. I love New York.

Q. Nobody is alone who cares for a pet.

R. Watering grass is sufficient for grass to grow.

S. If the butler did it, then the maid didn’t. The butler or the maid did it. If the maid did it, then the butler did it.

T. If math was interesting, then I would earn an ‘A.” Math isn’t interesting. Thus, I am not earning an “A.”

U. No alterations, redecorating, tacks, or nails shall be made in the building, unless written permission is obtained.

V. Babies are illogical. Nobody is despised who can manage a crocodile. Illogical people are despised.

W. If the population increases rapidly and production remains constant, then prices rise. If prices rise then the government will control prices. I am rich then I do not care about increases in prices. It is not true that I am not rich. Either the government does not control prices or I do not care about increases in prices. Therefore, it is not the case that the population increases rapidly and production remains constant.

X. Dean praises me only if I can be proud of myself. Either I do well in classes or I cannot be proud of myself. If I do my best in sports, then I cannot be proud of myself. Therefore, if Dean praises me, then I do my best in sports.

Y. If Winston or Halbert wins then Luke and Susan cry. Susan does not cry. Thus, Halbert does not win.

Z. If I enroll in the course and study hard, then I will earn acceptable grades. If I make satisfactory grades, then I am content. I am not content. Hence, either I did not enroll in this course or I did not study hard.

AA. If he goes to the party, he does not fail to brush his hair. To look fascinated is necessary to be tidy. If he is a sushi eater, then he has no self-command. If he brushes his hair, he looks fascinated. He wears white gloves only if he goes to the party. Having no self-command is sufficient to make one look untidy. Therefore, sushi eaters do not wear white gloves.

BB. No ducks waltz. No officer ever declined to waltz. All my poultry are ducks. Thus, Non of my poultry are officers.

CC. Everyone who is sane can do logic. None of your sons can do logic. No lunatics are fit to serve on the jury. Therefore, if he is your son, then he is not on the jury.

DD. The sum of an irrational number and a rational number is an irrational number.

EE. The product of two negative numbers is a positive number.

FF. The square root of a positive number is a positive number.

GG. [pic] only if [pic].

HH. If [pic] then [pic].

II. The square of a negative number is a positive number.

2. Translate the following into symbolic form (do not forget to define symbols representing prime statements) and supply a valid conclusion:

A. No kitten that loves fish is uneducable. No kitten without a tail will play with a gorilla. Kittens with whiskers always love fish. No educable kitten has green eyes. No kittens have tails unless they have whiskers.

B. Promise-breakers are untrustworthy. Alcohol drinkers are very verbose. A person who keeps a promise is honest. No teetotalers are pawnbrokers. One can trust a very loquacious person.

C. All the dated letters in this room are written on embossed paper. None of them are in black ink, except those that are written in the third person. I have not filed any of them that I can read. None of them that are written on one sheet are undated. All of them that are not crossed are in black ink. All of them written by Thomas Brown, Esq. Begin with “Dear Sir.” All of them written on embossed paper are filed. None of them written on more than one sheet are crossed. None of them that begin with “Dear Sir” are written in the third person.

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