CHAPTER 3 - ANSWERS


EXERCISES 3A


1. a. statement b. not a statement c. statement
d. not a statement e. not a statement f. statement
g. statement h. statement i. not a statement
  j. If the sentence is true, then it is false - but if it is false then it is true! Since the sentence can be neither true nor false, it is not a statement.
2. a. contradictory b. not contradictory c. not contradictory
d. contradictory e. not contradictory f. contradictory
g. contradictory h. not contradictory i. contradictory
j. not contradictory        
3. a. George Washington was the first President.
b. The temperature is less than 90 degrees.
c. Some of my friends are disloyal.
d. Some men can live by bread alone.
e. Sometimes Darlene misses breakfast.
f. It is not cold today.
g. No kind of fish is digestible to me.
h. Some of the stuff on TV is good these days.
i. For some actions there is no reaction.
j. My apple tree produced some oranges this year.
k. Sam missed some meetings.
l. Some of my children are not above average.
m. There are some things besides fear that we have to fear.
4. (There is more than one right answer to these problems.)
  a. I am not homeless.
b. U.H. did not lose the basketball game.
c. Erika is not sick.
d. All geckos are harmless.
e. Sly will not take fewer than five courses.
f. No good thing is endless.
g. Earl will not fail French.
h. Anything not a dame is different from a dame.

EXERCISES 3B


1. a. The horse is gone and the cow lows.
b. The horse is here and the gate is closed.
c. The cow lows or dusk falls.
d. The horse is gone and the gate is open and dusk falls.
e. The cow lows, or the horse is gone and dusk falls.
f. The cow lows or the horse is gone, and dusk falls.
g. It is not the case that the horse is gone and the gate is open.
h. Dusk falls and the horse is gone, or the gate is open.
i. The cow is silent or the horse is gone, and dusk does not fall.
j. The horse is gone and dusk falls, or the gate is closed and the cow is silent.
k. The gate is open or the horse is here or the cow lows.
l. The gate is closed, and it is not the case that the cow lows and dusk falls.
2. a. p Ù r   b. p Ù (r Ú s)   c. ~r Ù q   d. p Ù s Ù r
  e. (s Ú r) Ù ~q f. (p Ù r) Ú s g. (q Ù ~s) Ú (r Ù p) h. ~(s Ù r)
  i. (r Ú s) Ù (p Ù ~q) j. q Ú (~r Ù s Ù p)        
3. a. exclusive b. exclusive c. inclusive
d. inclusive e. inclusive f. exclusive
4. a. F   b. T   c. T
  d. T e. F f. T
  g. T h. F i. T
5. a. The last column in the table goes T, T, F, T.
b. The last column in the table goes F, F, T, F.
c. The last column in the table goes T, F, F, F.
6. He must vote for lower taxes, but not vote for fiscal reform.
7. Hint : Look at the similar table for negating a conjunction.
8. a. I will not study hard or not make an A on the test.
b. The boy is not over 16, and is not accompanied by a parent.
c. Peanut butter is not gooey or does not stick to the roof of your mouth.
d. I do not understand your position, or I am angry.
e. Jenny will visit both Paris and Rome.
f. The earth is flat, or it rests on the back of a turtle.
g. The resident of the apartment is home and awake.
h. Mary will not win the race, and will live.
9. a. The columns corresponding to the two statements both go F, T, T, T, T, T, T, T.
b. The columns corresponding to the two statements both go F, F, F, F, F, F, F, T.
10. a. The UH basketball team will lose to Rice or Fresno or Tulsa.
b. UH will beat Nevada, SMU, and Boise.
c. The team will not practice hard, or play dumb, or lose hope.
d. We will lose the game - and not try hard - and the coach will be pleased.
e. Andy and Ben and Carl and Dan will not make the all-conference team.
f. I will not enjoy the game or eat no popcorn or not yell with the cheerleaders or ignore the band.
11. a. p Ù q   b. p Ù ~q   c. p Ù q   d. ~p Ù ~q
  e. q Ù p f. q Ù ~p g. ~p Ù q h. q Ú p

EXERCISES 3C


1. a. If Fido barks then Felix jumps.
b. If Felix jumps then Tweety does not sing.
c. If Mickey runs, then Fido barks and Felix jumps.
d. If Tweety sings or Mickey runs, then Felix jumps.
e. If Fido does not bark then Tweety sings.
f. If Tweety sings, then Mickey runs and Felix jumps and Fido barks.
g. If Fido does not bark, then Mickey does not run and Tweety sings.
h. If Tweety does not sing and Mickey does not run, then Fido barks.
i. If Mickey runs and Felix jumps, then Fido barks and Tweety does not sing.
j. If Felix jumps and Mickey does not run, then Felix barks or Tweety sings.
  k. s → p   l. ~q → ~p   m. q → (r Ù ~s)   n. r → q
  o. s → (~r Ù ~p) p. q → (r Ú p) q. (p Ù r Ù s) → q r. (~s Ù ~p) → (~q Ú r)
2. a. F b. F c. F d. T e. T f. T
3. yes
4. a. If I listen to soothing music then I feel relaxed.
b. If Evelyn buys clothes, then Ala Moana is having a sale.
c. If an apple is green then it tastes sour.
d. If 3x + 1 = 7 then x = 2.
e. If you eat greasy foods then you gain weight.
f. If one is in his right mind then he will not wrestle a gorilla.
g. If interest rates rise then disposable income declines.
h. If I drink coffee in the evening then I lose sleep at night.
i. If you order a deluxe dinner then you get a free dessert.
j. If you qualify for a scholarship then you have a B average.
k. If your life is wild and reckless, then you age prematurely.
l. If a chicken has no saddle then you cannot ride it.
5. Make a truth table containing both sides of the equation, and check that the corresponding columns are the same.
6. a. You do not turn your back or the goat will butt you.
b. The milk was left inside the refrigerator, or it is spoiled.
c. Angie has left already, or she will be late.
d. I drink coffee in the morning, or I get sleepy.
e. You study hard or you make bad grades.
7. a. The pig has wings and it cannot fly.
b. Wages are up and unemployment is not down.
c. The window is open and it did not rain inside.
d. The car won't start and it is not out of gas.
e. Brad is not shy, and he will not ask Fay for a date.
f. The spaghetti sticks to the wall and it is not done.
g. The door is open and the professor is not having office hours.
h. Mr. Ramos is late for dinner, and Mrs. Ramos is happy.
8. a. If autumn is here, then the leaves have fallen.
If the leaves have not fallen, then autumn is not here.
If autumn is not here, then the leaves have not fallen.
b. If the news is on TV, then it is six o'clock.
If it is not six o'clock, then the news is not on TV.
If the news is not on TV, then it is not six o'clock.
c. If the beach is empty, then the surf is not up.
If the surf is up, then the beach is not empty.
If the beach is not empty, then the surf is up.
d. If you cannot read, then the light is off.
If the light is on, then you can read.
If you can read, then the light is on.
e. If the match will not light, it is wet.
If the match is dry, it will light.
If the match will light, it is dry.
f. If you are not informed, you do not read the paper.
If you read the paper, you are informed.
If you are informed, you read the paper.
g. The light is green only if the cars proceed.
The cars do not proceed only if the light is not green.
The light is not green only if the cars do not proceed.
h. The peacock wants his picture taken if he spreads his feathers.
The peacock does not spread his feathers if he does not want his picture taken.
The peacock does not want his picture taken if he does not spread his feathers.

EXERCISES 3D


1. a. tautology b. contingency c. contingency
d. contingency e. contradiction    
2. The last column in each truth table should contain only T's.
3. The last column in each truth table should contain at least one F.
4. valid 5. invalid 6. valid 7. invalid 8. invalid 9. valid
10. invalid 11. invalid 12. invalid 13. invalid 14. valid 15. valid
16. invalid 17. invalid 18. invalid 19. valid 20. valid 21. invalid
22. valid 23. invalid 24. valid 25. valid 26. invalid 27. invalid
28. valid 29. valid 30. valid 31. invalid 32. valid 33. valid
34. invalid 35. valid 36. invalid 37. invalid 38. valid 39. invalid

EXERCISES 3E


1. Your presents to me are not made of tin.
2. All my potatoes in this dish are old ones.
3. My poultry are not officers.
4. None of your sons are fit to serve on a jury.
5. Jenkins is inexperienced.
6. This dish is unwholesome.
7. No hedgehog takes in the Times.
8. No jug in this cupboard will hold water.
9. These apples were grown in the sun.
10. All hummingbirds are small.
11. No scentless flowers please me.
12. All gluttons, who are children of mine, are unhealthy.
13. An egg of the Great Auk is not to be had for a song.
14. No bird in this aviary lives on mince pies.
15. None but red haired boys learn Greek in this school.
16. Wedding cake always disagrees with me.
17. All the romances in this library are well written.
18. No pawnbroker is dishonest.
19. Shakespeare was clever.
20. Rainbows are not worth writing odes to.
21. No kitten with green eyes will play with a gorilla.
22. Donkeys are not easy to swallow.
23. No heavy fish is unkind to children.
24. Opium eaters never wear white kid gloves.
25. I always avoid a kangaroo.