?Compound Proposition questions

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Homework for Chapter 5 Compound Proposition
Exercise A. Negation
Instruction: Convert each of the following negative propositions into one in the standard form of negative
Example: Doing laundry is not fun.
Answer: It is not the case that doing laundry is fun.
1. It is not cheap to dine out every day.
2. The hijackers were not from Cuba.
3. Dizzie Dean was not a pitcher.
4. Jens proposal is unacceptable.
5. Susan has gone irrational.
6. This can of baby formula is a non-dairy product.
7. Larry is disappointed in those newly hired employees.
8. Bribery in business operation is illegal.
9. American wireless service systems are incompatible.
10. It is impossible to leave the Earth by pulling your hair.
1
Exercise B. Conjunctive Proposition
There are two types of questions in this section. Please follow the instructions for each below.
B-1: Convert the embedded propositions into conjuncts of a complex conjunctive proposition.
Instruction: For each of the following propositions, identify the embedded propositions and form a complex
Example 1: Information about DNA, RNA, and the proteins found in different species can be compared
to establish taxonomic relationships.
Answer: Information about DNA, RNA, and the proteins are found in different species and the
information can be compared to establish taxonomic relationships.
Example 2: The dog, whose owner is Bob, is driving a car owned by David on US 53.
Answer: [(The dogs owner is Bob and the dog is driving a car) and the car is owned by David]
and the dog is on US 53.
1. The junior executives who asked for a raise were summarily dismissed.
2. Snakes, which are reptiles without legs, kill a large number of rodents.
3. Sometime another factor, which was not easily identified, was involved in the chemical reaction.
4. My most valuable possession is an old, slightly warped blond guitar, which is the first instrument I
learned how to play.
5. Gregory, my beautiful gray Persian cat, walks with pride and grace, performing a dance of disdain.
B-2: Convert variants of conjunction into the standard forms.
Instruction: Convert each of the following variants of conjunctive propositions into one in the standard form of
Example: The Greeks won the battle but lost the war.
Answer: The Greeks won the battle and The Greeks lost the war.
2
1. Dan went swimming even though the water was freezing.
2. Tom came; however, the coach did not show up.
3. Although George works hard, he never does well.
4. That man is singing while he is running.
5. Fred and Nancy are chatting.
Exercise C. Disjunctive Proposition
There are two types of questions in this section. Please follow the instructions for each below.
C-1: Distinguish between inclusive and exclusive disjunction.
Instruction: For each of the following disjunctive propositions, indicate whether it is an inclusive or exclusive
Example: Either Leslie is not sad or she’s a good actor.
1. I will drive her to her house or she will take a taxi.
2. You can rent the movie or read the book.
3. Either it rained or the Wilsons’ barbecue went as planned.
4. Julianne will try for the green with a long iron, or else chip out onto the fairway.
3
5. Either Carol will win or Jim will win the gold medal.
C-2: Convert variants of disjunction into the standard one
Instruction: Convert each of the following variants of disjunctive propositions into one in the standard form of
Example: Ill take either Project A or Project B.
Answer: Either Ill take Project A or Ill take Project B.
1. I’m busy; otherwise I’d accept your invitation.
2. You’ll have to wear warm clothes; otherwise you’ll catch a cold.
3. At least one of SAT and ACT tests is accepted by universities.
4. I will be disappointed unless I win.
5. Unless I work all night, I won’t finish the paper.
Exercise D. Conditional Proposition
Instruction: Convert each of the following variants of conditional propositions into one in the standard form of
Example: We will see the Nutcracker Suite if we get tickets.
Answer: If we get tickets, then we will see the Nutcracker Suite.
1. I will read the paper with breakfast as long as it arrives in time.
2. I will wear the shoes provided they fit.
4
3. Hell miss the game if he goes home for dinner.
4. The Wades look for a cheap hotel room in case they cannot find someone to stay with for free.
5. They will be playing baseball in the snow in the event that spring does not come soon.
6. The president will be re-elected only if there is no a recession this year.
7. I will not get my work done if the road construction is not finished within two days.
8. He will quit his job only if he gets a big raise.
9. Suppose that Carol wins, we will hold a big party to celebrate.
10. The bill will pass only if the liberals are happy with it.
Exercise E. Biconditional
Instruction: Convert each of the following variants of biconditional propositions into one in the standard form
Example: Ill buy the boots just in case they fit.
1. We’ll settle out of court if but only if they agree to our terms.
2. The bill will pass if but only if the conservatives support it.
5
3. We put a man on the moon just in case you put a man on Venus.
4. The president will be re-elected if but only if there is no foreign affairs fiasco.
5. Norton attends the party just in case Megan does.
6
Homework for Chapter 5 Compound Proposition
Exercise A. Negation
Instruction: Convert each of the following negative propositions into one in the standard form of negative
Example: Doing laundry is not fun.
Answer: It is not the case that doing laundry is fun.
1. It is not cheap to dine out every day.
2. The hijackers were not from Cuba.
3. Dizzie Dean was not a pitcher.
4. Jens proposal is unacceptable.
5. Susan has gone irrational.
6. This can of baby formula is a non-dairy product.
7. Larry is disappointed in those newly hired employees.
8. Bribery in business operation is illegal.
9. American wireless service systems are incompatible.
10. It is impossible to leave the Earth by pulling your hair.
1
Exercise B. Conjunctive Proposition
There are two types of questions in this section. Please follow the instructions for each below.
B-1: Convert the embedded propositions into conjuncts of a complex conjunctive proposition.
Instruction: For each of the following propositions, identify the embedded propositions and form a complex
Example 1: Information about DNA, RNA, and the proteins found in different species can be compared
to establish taxonomic relationships.
Answer: Information about DNA, RNA, and the proteins are found in different species and the
information can be compared to establish taxonomic relationships.
Example 2: The dog, whose owner is Bob, is driving a car owned by David on US 53.
Answer: [(The dogs owner is Bob and the dog is driving a car) and the car is owned by David]
and the dog is on US 53.
1. The junior executives who asked for a raise were summarily dismissed.
2. Snakes, which are reptiles without legs, kill a large number of rodents.
3. Sometime another factor, which was not easily identified, was involved in the chemical reaction.
4. My most valuable possession is an old, slightly warped blond guitar, which is the first instrument I
learned how to play.
5. Gregory, my beautiful gray Persian cat, walks with pride and grace, performing a dance of disdain.
B-2: Convert variants of conjunction into the standard forms.
Instruction: Convert each of the following variants of conjunctive propositions into one in the standard form of
Example: The Greeks won the battle but lost the war.
Answer: The Greeks won the battle and The Greeks lost the war.
2
1. Dan went swimming even though the water was freezing.
2. Tom came; however, the coach did not show up.
3. Although George works hard, he never does well.
4. That man is singing while he is running.
5. Fred and Nancy are chatting.
Exercise C. Disjunctive Proposition
There are two types of questions in this section. Please follow the instructions for each below.
C-1: Distinguish between inclusive and exclusive disjunction.
Instruction: For each of the following disjunctive propositions, indicate whether it is an inclusive or exclusive
Example: Either Leslie is not sad or she’s a good actor.
1. I will drive her to her house or she will take a taxi.
2. You can rent the movie or read the book.
3. Either it rained or the Wilsons’ barbecue went as planned.
4. Julianne will try for the green with a long iron, or else chip out onto the fairway.
3
5. Either Carol will win or Jim will win the gold medal.
C-2: Convert variants of disjunction into the standard one
Instruction: Convert each of the following variants of disjunctive propositions into one in the standard form of
Example: Ill take either Project A or Project B.
Answer: Either Ill take Project A or Ill take Project B.
1. I’m busy; otherwise I’d accept your invitation.
2. You’ll have to wear warm clothes; otherwise you’ll catch a cold.
3. At least one of SAT and ACT tests is accepted by universities.
4. I will be disappointed unless I win.
5. Unless I work all night, I won’t finish the paper.
Exercise D. Conditional Proposition
Instruction: Convert each of the following variants of conditional propositions into one in the standard form of
Example: We will see the Nutcracker Suite if we get tickets.
Answer: If we get tickets, then we will see the Nutcracker Suite.
1. I will read the paper with breakfast as long as it arrives in time.
2. I will wear the shoes provided they fit.
4
3. Hell miss the game if he goes home for dinner.
4. The Wades look for a cheap hotel room in case they cannot find someone to stay with for free.
5. They will be playing baseball in the snow in the event that spring does not come soon.
6. The president will be re-elected only if there is no a recession this year.
7. I will not get my work done if the road construction is not finished within two days.
8. He will quit his job only if he gets a big raise.
9. Suppose that Carol wins, we will hold a big party to celebrate.
10. The bill will pass only if the liberals are happy with it.
Exercise E. Biconditional
Instruction: Convert each of the following variants of biconditional propositions into one in the standard form
Example: Ill buy the boots just in case they fit.
1. We’ll settle out of court if but only if they agree to our terms.
2. The bill will pass if but only if the conservatives support it.
5
3. We put a man on the moon just in case you put a man on Venus.
4. The president will be re-elected if but only if there is no foreign affairs fiasco.
5. Norton attends the party just in case Megan does.
6

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