More Basic Concepts and Practice Test 1

Introduction to Logic: Class 2

Small Group Exercise

Each group should

• agree on answers to all the problems in their section.

• write up an answer sheet for me with all your names and agreed on answers on it.

• put your answers on the board.

ContradictionA contradiction is a statement that cannot possibly be true because of its basic logic.

• He was both running and sitting still at the same time.

• The colorless object was bright green.

• The circle had sharp corners.

TautologyA tautology is a statement that must be true because of its basic logic.• All bachelors are unmarried men.

• An invisible object can’t be seen.

• All triangles have three sides.

Contingent StatementA statement that can be either true or false, depending on the way the world is apart from the sentence.

• It is raining right now.

• I am a bachelor

• This triangle is green

Logically equivalent statementsTwo statements are logically equivalent if they both have to be true, or both have to be false, because of their basic logic.

It is raining Water is falling from the sky

Susan is taller than Bob Bob is shorter than Susan

Peter Parker loves Mary Jane Watson

Spider-man loves Mary Jane Watson

Logically equivalent statements effectively say the same thing.

Consistent statementsA set of statements is consistent if it is logically possible for them all to be true.

These sentences are consistent

• This shape is a triangle

• This shape is red

• If something is a red, then it must have three sides

These sentences are not consistent:

• Mark is taller than Julie

• Julie is taller than Kim

• Kim is taller than Mark.

These sentences are consistent

• This shape is a triangle

• This shape is red

• If something is red, then it must have four sides.

Practice Test 1

1. What is logic? Explain what logic is for the purposes of this course in 30 to 50 words.

1. What is logic? Explain what logic is for the purposes of this course in 30 to 50 words.Logic is the study of virtue in argument. In other words, it is the study of a kind of virtuous persuasion, which is likely to lead to true beliefs. Logic should be contrasted with rhetoric, which is the study of effective persuasion.

This is a sample answer. Answers that get full credit can have phased many different ways as long as they capture the same basic idea.

a. Logic takes practice. b. All mimsy were the borogoves and the

mome raths outgrabe.” c. Frivolity is a stern taskmaster. d. How much time do you spend on

homework each week? e. If you are done, but down your pencil and

look bored.

2. Which of the following are statements in the logical sense? (Mark all that apply.)

a. Logic takes practice. b. “All mimsy were the borogoves and the

mome raths outgrabe.” —Lewis Carroll c. “Frivolity is a stern taskmaster.”

--Bill Griffithd. How much time do you spend on

homework each week? e. If you are done, but down your pencil and

look bored.

2. Which of the following are statements in the logical sense? (Mark all that apply.)

f. my small brown dog.

g. You vacuous, toffee-nosed, malodorous pervert!

h. You are a vacuous, toffee-nosed, malodorous pervert.

i. Don’t skip this question.

j. Do you understand the concept “Sentence” as it is defined in logic?

2. Which of the following are statements in the logical sense? (Mark all that apply.)

2. Which of the following are statements in the logical sense? (Mark all that apply.)

f. my small brown dog.

g. You vacuous, toffee-nosed, malodorous pervert!

h. You are a vacuous, toffee-nosed, malodorous pervert.

i. Don’t skip this question.

j. Do you understand the concept “Sentence” as it is defined in logic?

3. Which of the following is the best definition of an argument? Check one.

a. An argument is a connected series of sentences designed to convince an audience of another sentence

b. An argument is the automatic gainsaying of whatever someone else says.

c. An argument is when two people disagree with each other.

d. An argument is an intellectual process based on contradiction.

3. Which of the following is the best definition of an argument? Check one.

a. An argument is a connected series of sentences designed to convince an audience of another sentence

b. An argument is the automatic gainsaying of whatever someone else says. -7

c. An argument is when two people disagree with each other. -10

d. An argument is an intellectual process based on contradiction. -4

4. Explain the concept of validity in logic in 10 to 20 words

4. Explain the concept of validity in logic in 10 to 20 words

Validity is a property of arguments where the conclusion must be true if the premises are true.

This is a sample answer. Answers that get full credit can have phased many different ways as long as they capture the same basic idea.

4. Explain the concept of validity in logic in 10 to 20 words

An argument is valid if it is impossible for the premises to be true and the conclusion false.

This is a sample answer. Answers that get full credit can have phased many different ways as long as they capture the same basic idea.

c. If the woolly mammoth couldn’t adapt to the warmer climate, it went extinct.The wooly mammoth is extinct. The wooly mammoth couldn’t adapt to warmer climate.

5. Which of the following arguments are valid? Mark all “valid” or “invalid.”

If I thought this question was unfair, I wouldn’t ask it.I am asking this questionI think it is fair.

a.

b. Some people are not dogsAll dogs are mammals Some people are not mammals.

c. If the woolly mammoth couldn’t adapt to the warmer climate, it went extinct.

The wooly mammoth is extinct. The wooly mammoth couldn’t adapt to warmer climate.. invalid

5. Which of the following arguments are valid? Mark all “valid” or “invalid.”

If I thought this question was unfair, I wouldn’t ask it.I am asking this questionI think it is fair. valid

a.

b. Some people are not dogsAll dogs are mammals Some people are not mammals. invalid

6. Put the following argument in canonical form. Be sure to eliminate indicator words and phrases and other excess words. Below the argument list any premise or conclusion indicator words.

Fifty years ago there were 435 congressmen and 96 senators. Today there are 435 congressmen and 100 senators. The number of legislators is fixed; the legislature’s workload has grown exponentially. So the legislature’s work is increasingly done elsewhere, no matter what you read in you high-school civics text.

---George F. Will, “More Government, Less Control,” Newsweek (July 4, 1963) Quoted in Gary Jason Introduction to Logic

1: Fifty years ago there were 435 congressmen and 96 senators.

2: Today there are 435 congressmen and 100 senators.

3: The number of legislators is fixed; the legislature’s workload has grown exponentially.

The legislature’s work is increasingly done elsewhere

“So” is a conclusion indicator word.

7. Mark the following “Tautology” “Contingent” or “Contradiction.”

a. Elephants dissolve in water.

b. Wood is a light, durable substance useful for building things.

c. If wood made good building material, it would be useful for building things.

d. I live in a three story building that is two stories tall.

e. If gerbils were mammals they would nurse their young.

7. Mark the following “Tautology” “Contingent” or “Contradiction.”

a. Elephants dissolve in water. Contingent

b. Wood is a light, durable substance useful for building things. Contingent

c. If wood made good building material, it would be useful for building things. Tautology

d. I live in a three story building that is two stories tall. Contradiction

e. If gerbils were mammals they would nurse their young. Tautology

A logically true statement or tautology is a statement that must always be true because of the way it is constructed.

Examples:

“Either it is raining, or it is not.”

“All bachelors are unmarried.”

A contradiction is a statement that must always be false because of the way it is constructed.

Examples:

“It is both raining and not raining.”

“This figure is a round square”

A contingent statement is a statement that could be true or false depending on the way the world is.

Examples:

“It is raining right now.”

“Bob is a bachelor.”

8. Which of the following pairs of sentences are logically equivalent? Mark each “Logically equivalent” or “not logically equivalent.”

a. Musicians expect you to take them seriously

Lady Gaga does not expect you to take her seriously.

b. Musicians expect you to take them seriously

Janelle Monáe expects you to take her seriously.

c. Elephants have inefficient digestive systems

Elephants do not digest their food very well.

d. Elephants are bigger than lions

Lions are smaller than elephants.

e. The Eurasian elephant is a herbivore.

All elephants are herbivores.

8. Which of the following pairs of sentences are logically equivalent? Mark each “Logically equivalent” or “not logically equivalent.”

a. Musicians expect you to take them seriously

NLE Lady Gaga does not expect you to take her seriously.

b. Musicians expect you to take them seriously

NLE Janelle Monáe expects you to take her seriously.

c. Elephants have inefficient digestive systems

LE Elephants do not digest their food very well.

d. Elephants are bigger than lions

LE Lions are smaller than elephants.

e. The Eurasian elephant is a herbivore.

NLE All elephants are herbivores.

Two statements are logically equivalent if they must always have the same truth value.

Examples:

“Susan is shorter than Bob” and “Bob is taller than Susan”

“Bob is an unmarried man” and “Bob is a bachelor.”

9. Consider the following set of sentences.

M1. The mail will not come on Monday.M2. Monday is a holiday.

M3. If Monday is a holiday, the mail will not come.M4. The mail will come on Monday.

Which combinations of sentences form consistent sets? Mark each “consistent” or “inconsistent.”

a. M1, M2, and M3b. M2, M3, and M4. c. M2 and M3. d. M1 and M4e. M1, M2, M3, and M4.

9. Consider the following set of sentences.

M1. The mail will not come on Monday.M2. Monday is a holiday.

M3. If Monday is a holiday, the mail will not come.M4. The mail will come on Monday.

Which combinations of sentences form consistent sets? Mark each “consistent” or “inconsistent.”

a. M1, M2, and M3 Consistent b. M2, M3, and M4. Inconsistent c. M2 and M3. Consistent d. M1 and M4 Inconsistent e. M1, M2, M3, and M4. Inconsistent

A set of statements is inconsistent if is impossible for them to all be true at the same time.

Example:

“Mark is taller than Julie”

“Julie is taller than Kim”

“Kim is taller than Mark.”

10. Which of the following are possible? (Mark all that apply)

a. A valid argument, whose premises are all tautologies, and whose conclusion is contingent.

b. A valid argument with true premises and a false conclusion.

c. A consistent set of sentences which contains two sentences that are not logically equivalent.

d. A consistent set of sentences, all of which are contingent.

e. A false tautology.

10. Which of the following are possible? (Mark all that apply)

a. A valid argument, whose premises are all tautologies, and whose conclusion is contingent.

b. A valid argument with true premises and a false conclusion.

c. A consistent set of sentences which contains two sentences that are not logically equivalent.

d. A consistent set of sentences, all of which are contingent.

e. A false tautology.