Homework for Chapter 6 Deduction with Compound Proposition

| September 12, 2019


Homework for 
Chapter 6 Deduction with Compound Proposition

Course CodePHI 110SectionName

Exercise A. Identify Types of Reasoning

In this exercise you are given a list of reasoning samples and asked to determine what type of reasoning each sample is. Please indicate your answer in the space to the right of the word “Answer”.

Example 1: Information about DNA, RNA, and the proteins found in different species can be compared to establish taxonomic relationships. Therefore, information about DNA, RNA, and the proteins are found in different species.

Answer: Reasoning from a conjunctive proposition

Example 2: We will see the movie if we get tickets. We get tickets. Therefore, we will see the movie. Answer: Reasoning from a conditional proposition (Modus Ponens)

We’ll settle out of court if and only if they agree to our terms. Since they don’t agree to our terms, we won’t settle out of court.

Answer:

David went swimming. The water was freezing. So, David went swimming even though the water was freezing.

Answer:

Either I will graduate in May or in January. I will graduate in January. So, I will not graduate in May.

Answer:

I will go skiing only if you will teach me, but since you are unwilling to teach me, I won’t go.

Answer:

I will be able to travel to Europe if the exchange rate remains favorable. And I will be able to travel to Europe only if the exchange rate remains favorable. Therefore, I will be able to travel to Europe if and only if the exchange rate remains favorable.

Answer:

The junior executives who asked for a raise were summarily dismissed. So, some junior executives asked for a raise.

Answer:

The next Olympics may be held in Atlanta, Georgia. And Athens, Greece also applied for holding the game. So, either the next Olympics will be held in Atlanta, Georgia or in Athens, Greece.

Answer:

If the account of creation in Genesis is literally correct, then the sun was not created until the fourth day. If the sun was not created until the fourth day, then the word “day” cannot be taken literally to mean one cycle of sunrise and sunset. Therefore, if the account of creation in Genesis is literally correct, the word “day” cannot be taken literally to mean one cycle of sunrise and sunset.

Answer:

John is either a knave or a fool. He is not a fool. Therefore, he is a knave.

Answer:

If God had wanted us to fly, He would have given us wings. He has not given us wings. Therefore, He did not want us to fly.

Answer:

Exercise B. Evaluating Conjunctive Reasoning

In this exercise you are given a list of conjunctive reasoning samples and asked to determine which one is deductively valid and which one is not. Please indicate your answer in the space to the right of the word “Answer”.

Example 1: Information about DNA, RNA, and the proteins found in different species can be compared to establish taxonomic relationships. Therefore, information about DNA, RNA, and the proteins are found in different species.

Answer: Deductively valid

Example 2: Information about DNA, RNA, and the proteins are found in different species. Therefore, information about DNA, RNA, and the proteins found in different species can be compared to establish taxonomic relationships.

Answer: Deductively invalid

Snakes, which are reptiles without legs, kill large number of rodents. So, snakes kill a large number of rodents.

Answer:

Sometime some other factors were involved in the chemical reaction. Those factors were not easily identified. Therefore, sometime some other factors, which were not easily identified, were involved in the chemical reaction.

Answer:

My most valuable possession is an old guitar. It is the first instrument I learned how to play. So, my most valuable possession is an old, slightly warped blond guitar, which is the first instrument I learned how to play.

Answer:

Gregory, my beautiful gray Persian cat, walks with pride and grace, performing a dance of disdain. So, my beautiful gray Persian cat walks with pride and grace.

Answer:

Dan went swimming. So, Dan went swimming even though the water was freezing.

Answer:

Tom arrived at the meeting room on time; however, his coach did not show up. So, Tom’s coach did not go to the meeting.

Answer:

George never does well on an individual project. Therefore, although George works hard, he never does well on an individual project.

Answer:

Fred attended the five-person meeting chaired by Nancy. So, Fred must have met Nancy.

Answer:

Fred and Nancy are talking on the phone. Therefore, Fred and Nancy are having a telephone meeting.

Answer:

Jen is running. Jen is singing. So, Jen is singing while she is running.

Answer:

Exercise C. Evaluating Disjunctive Reasoning

In this exercise you are given a list of disjunctive reasoning samples and asked to determine which one is deductively valid and which one is not. Please indicate your answer in the space to the right of the word “Answer”.

Example 1: Either Leslie is not sad or she’s a good actor. Leslie is a good actor. Therefore, she is sad.

Answer: Deductively invalid

Example 2: Either I will graduate in May or in January. I will graduate in January. So, I will not graduate in May.

Answer: Deductively valid

The next Olympics may be held in Atlanta, Georgia. And Athens, Greece also applied for holding the game. So, either the next Olympics will be held in Atlanta, Georgia or in Athens, Greece.

Answer:

Either Jen or Sara will win the gold medal. Jen will win the gold medal. Therefore, Sara will not win the gold medal.

Answer:

Either Jen or Sara will win a gold medal. Sara will win a gold medal. Therefore, Jen will not win a gold medal.

Answer:

Either wealth is evil or it is good. Wealth is not evil. Therefore, wealth is good.

Answer:

She will not graduate unless she passes geology. She will pass geology. Therefore, she will not graduate.

Answer:

The President was obligated to notify Congress about sending troops and ships to the Persian Gulf. So, the President was obligated to notify Congress about sending troops and ships to the Persian Gulf unless considerations of national security prevented him.

Answer:

The star of the movie was either Madonna or someone who looked very much like her. The star was not someone who looked very much like her. Therefore, the star was Madonna.

Answer:

The new budget will either create a huge deficit or stimulate the economy. The new budget will create a

huge deficit. Therefore, the new budget will not stimulate the economy.

Answer:

Either Carol rents the movie or she reads the book. Carol reads the book. Therefore, she does not rent the movie.

Answer:

At least one of the SAT and ACT tests is accepted by universities. The ACT is accepted by universities. Therefore, the SAT test is not accepted by universities.

Answer:

Exercise D. Evaluating Conditional Reasoning

In this exercise you are given a list of conditional reasoning samples and asked to determine which one is deductively valid and which one is not. Please indicate your answer in the space to the right of the word “Answer”.

Example 1: I will read the paper with breakfast as long as it arrives in time. The paper arrives in time. Therefore, I will read the paper with breakfast.

Answer: Deductively valid

Example 2: I will wear the shoes provided they fit. The shoes don’t fit. Therefore, I will not wear them.

Answer: Deductively invalid

I will go skiing only if you will teach me, but since you are unwilling to teach me, I won’t go.

Answer:

I will go swimming if a lifeguard is on duty. A lifeguard is not on duty. Therefore, I will not go swimming.

Answer:

If I win the lottery, then I’ll quit my job. If I quit my job, then I’ll be unemployed. Therefore, I will be unemployed.

Answer:

If there were no reindeer, Santa Claus would not exist. Santa Claus does exist. Therefore, there are reindeer.

Answer:

If ice were heavier than water, ponds would freeze solid in winter. Ice is not heavier than water. Therefore, ponds do not freeze solid in winter.

Answer:

If Israel allows the creation of a Palestinian state on the West Bank, its own survival will be jeopardized. If Israel’s survival is jeopardized, violence in the Middle East will increase. Therefore, if Israel allows the creation of a Palestinian state on the West Bank, violence in the Middle East will increase.

Answer:

If his clothing carries traces of radioactivity, then he was in the area. His clothing carries no traces of radioactivity. Therefore, he was not in the area.

Answer:

If the account of creation in Genesis is literally correct, then the sun was not created until the fourth day. If the sun was not created until the fourth day, then the word “day” cannot be taken literally to mean one cycle of sunrise and sunset. Therefore, if the account of creation in Genesis is literally correct, the word “day” cannot be taken literally to mean one cycle of sunrise and sunset.

Answer:

If the human mind were an information processing system like a computer, then creativity would be hard to explain. Creativity is hard to explain. Therefore, the human mind is not an information processing system like a computer.

Answer:

If organic molecules can form spontaneously in a liquid containing the chemical building blocks, then life could have emerged in the oceans of the earth without outside intervention. Organic molecules can form spontaneously in a liquid containing the chemical building blocks. Therefore, life could have emerged in the oceans of the earth without outside intervention.

Answer:

Exercise E. Evaluating Biconditional Reasoning

In this exercise you are given a list of biconditional reasoning samples and asked to determine which one is deductively valid and which one is not. Please indicate your answer in the space to the right of the word “Answer”.

Example 1: I’ll buy the boots just in case they fit. The boots do not fit. Therefore, I won’t buy them.

Answer: Deductively valid.

Example 2: If we settle out of court, they must agree to our terms. If they do agree to our terms, we’ll settle out of court. Therefore, either we settle out of court or they agree to our terms.

Answer: Deductively invalid.

I will be able to travel to Europe if and only if the exchange rate remains favorable. I won’t be able to go to Europe. Therefore, the exchange rate did not remain favorable.

If you owe the bank a hundred dollars, it is your problem; but if you owe them a million dollars, it is their problem. Therefore, you owe the bank a hundred dollars if and only if it is your problem

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