PHI 120- Quizzes 1-4

It is not the case that either Lee Ann or Mary Lynn is a vegetarian. Select the Well Formed Formula that best represents the argument above:

~ ( L v M)

Use your knowledge of conjunction, disjunction, negation and truth tables to determine whether the following arguments are valid or invalid. P ⊃ ( P v S ) P / S

Invalid

If it walks like a duck and talks like a duck, then it's a duck. Select the Well Formed Formula that best represents the argument above:

( W · T ) ⊃ D

If Carly works hard and is not distracted, then she will get done on time. Select the Well Formed Formula that best represents the argument above:

( W · ~ D ) ⊃ T

1 All fires need oxygen. 2 There is no oxygen in that room. So, 3 there is no fire in that room. Determine the correct diagram for each argument.

(1,2) --> 3

1 Stealing someone's personal property is illegal. 2 Stealing someone's intellectual property is illegal. So, 3 you should respect all kinds of property. 4 This respect will lead to a more civil society. Determine the correct diagram for each argument.

(1,2) --> 3 --> 4

1 Carly tossed a coin ten times, and 2 in each case it came up heads. 3 I have a feeling that it is a trick coin. So, 4 I predict the next toss will be heads. Determine the correct diagram for each argument.

(1,2) --> 3 --> 4

1 More and more people throughout the world will soon buy electronic items, because 2 the cost of electronic items, such as televisions, computers, and cell phones, goes down every year, and 3 the quality of the electronic products goes up every year. Determine the correct diagram for each argument.

(2,3) --> 1

Use your knowledge of truth tables to determine if the following sets of statements are contradictory, consistent, or inconsistent. P ⊃ Q P v ~ Q

Consistant

The last line of each example gives the reference to the line or lines needed for its derivation. You are to determine the correct rule of inference. 1. ( ~ R ⊃ S ) v P 2. ~ ( ~ R ⊃ S ) 3. P 1, 2, ___

DS

The last line of each example gives the reference to the line or lines needed for its derivation. You are to determine the correct rule of inference. 1. C ⊃ S 2. S ⊃ T 3. C ⊃ T 1, 2, ___

HS

~ L ⊃ ( ~ P v ~ Q ) Identify the main operator.

Horseshoe

Use your knowledge of truth tables to determine if the following two statements are logically equivalent. ~ R · ~ S ~ ( R v S )

Logically equivalent

Use your knowledge of truth tables to determine if the following two statements are contradictory, consistent, or inconsistent. ~ A · B A · ~ B

Inconsistant

Determine whether the following completed proofs are correct or incorrect. 1. ( T v S ) v ~ R 2. ~ ( T v S ) · ( P v Q ) / ~ R 3. ~ ( T v Q ) 2, Simp 4. ~ R 1, 3, DS

Incorrect

Determine whether the following completed proofs are correct or incorrect. 1. T v R 2. [ ( T v R ) v ( S · P ) ] ⊃ ( Q · S ) / Q · S 3. ( T v R ) ⊃ ( S · P ) 1, Add 4. Q · S 2, 3, MP

Incorrect

"The coin came up tails ten times in a row. It probably will come up heads on the next toss." The argument above is: deductive or indicative

Inductive

Use your knowledge of conjunction, disjunction, negation and truth tables to determine whether the following arguments are valid or invalid. ( J v Y ) v A ~ Y / J

Invalid

Use your knowledge of truth tables to determine if the pairs of statements are logically equivalent. ( S · R) v ( S · W) S · ( R v W )

Logically equivalent

The last line of each example gives the reference to the line or lines needed for its derivation. You are to determine the correct rule of inference. 1. ( R · B ) ⊃ ( W v G ) 2. R · B 3. W v G 1, 2, ___

MP

The last line of each example gives the reference to the line or lines needed for its derivation. You are to determine the correct rule of inference. 1. ~ R ⊃ ( S ⊃ T ) 2. ~ R 3. S ⊃ T 1, 2, ___

MP

The last line of each example gives the reference to the line or lines needed for its derivation. You are to determine the correct rule of inference. 1. R ⊃ (S v P) 2. ~ (S v P) 3. ~ R 1, 2, ___

MT

The last line of each example gives the reference to the line or lines needed for its derivation. You are to determine the correct rule of inference. 1. R ⊃ S 2. ~ S 3. ~ R 1, 2, ___

MT

L ~ ⊃ P Determine whether the above arrangement of logical operator symbols makes a Well Formed Formula (WFF).

Not a WFF

The following questions refer to the counterexample method. No cars are trucks. All trucks are heavy equipment. Therefore, no cars are heavy equipment.

No C are T. All T are H. No C are H.

If ( P v Q ) is true, then what can you say about the truth value of P?

P can be either true or false

It will rain tomorrow and we will not go to the beach. Select the Well Formed Formula that best represents the argument above:

R · ~ B

( L · ~ P ) · Q Identify the main operator.

Right dot

If ( P · Q ) is false, then what can you say about the truth value of P?

P can be either true or false

Which one of the following substitutions shows the argument in the question above as invalid?

S = cats, P = mammals, and R = dogs

Which one of the following substitutions shows the argument in the question above as invalid?

C = cats, T = dogs, and H = mammals.

If ( P v Q ) is false, then what can you say about the truth value of P?

P is false

1 Good study habits are required for success in college. 2 It is also important that you get enough sleep every night. 3 Also, try to participate in class discussion as much as possible. 4 Doing these things will make college life more enjoyable. Determine the correct diagram for each argument.

1, 2, 3 --> 4

The following questions refer to the counterexample method. All squares are parallelograms. All rectangles are parallelograms. Therefore, all squares are rectangles.

All S are P. All R are P. All S are R.

More damage was done last year from hurricanes than earthquakes. There was $100 million damage last year from hurricanes. There was $70 million damage last year from earthquakes. The collection of statements above are: argument or explanation

Argument

My aunt invested $1000 in the stock market last month. The TV announcer said that the average stock has lost 20% in value this month. I guess we know what that means. My aunt probably lost $200 in stock value. Argument or explanation

Argument

Since there is biological evidence that the genetic characteristics for nonviolence have been selected over time by the species, we should see an overall decrease in violence among humans worldwide in the coming centuries. The collection of statements above is: argument or explanation

Argument

"Hamburgers are loaded with saturated fat and sodium. Pizza is loaded with saturated fat and sodium. Too much saturated fat and sodium is harmful to your heart. Jim takes in too much saturated fat and sodium. It follows that Jim is harming his heart." In this argument, "Jim is harming his heart" is: premise or conclusion

Conclusion

The last line of each example gives the reference to the line or lines needed for its derivation. You are to determine the correct rule of inference. 1. ( P ⊃ ~ Q ) · ( R ⊃ ~ S ) 2. P v R 3. ~ Q v ~ S 1, 2, ___

CD

The last line of each example gives the reference to the line or lines needed for its derivation. You are to determine the correct rule of inference. 1. ( W ⊃ S ) · ( V ⊃ O ) 2. W v V 3. S v O 1, 2, ___

CD

The last line of each example gives the reference to the line or lines needed for its derivation. You are to determine the correct rule of inference. 1. [ ( P ⊃ R ) ⊃ S ] · [ ( Q ⊃ R ) ⊃ T ] 2. ( P ⊃ R ) v ( Q ⊃ R ) 3. S v T 1, 2, ___

CD

"Building fuel-efficient cars helps reduce gasoline consumption. Dependency on foreign oil for gasoline production is a drain on the economy. Offshore oil drilling is dangerous. Oil spills through faulty drilling are hazardous to life; so are large tanker spills. Carbon emissions are hurting the environment. We need to start building more fuel-efficient cars" In this argument, "We need to start building more fuel-efficient cars" is a: premise or conclusion

Conclusion

The last line of each example gives the reference to the line or lines needed for its derivation. You are to determine the correct rule of inference. 1. P ⊃ S 2. ( R ⊃ S ) v ( R ⊃ Q ) 3. ( P ⊃ S ) · [ ( R ⊃ S ) v ( R ⊃ Q ) ] 1, 2, ___

Conj

Use your knowledge of truth tables to determine if the following two statements are contradictory, consistent, or inconsistent. S ≡ U S v U

Consistant

Use your knowledge of truth tables to determine if the following two statements are contradictory, consistent, or inconsistent. A v ~ B ~ A v B

Consistent

Determine whether the following completed proofs are correct or incorrect. 1. ( T ⊃ P ) · ( S v Q ) 2. R ⊃ T / R ⊃ P 3. T ⊃ P 1, Simp 4. R ⊃ P 2, 3, HS

Correct

Determine whether the following completed proofs are correct or incorrect. 1. ~ T 2. R ⊃ S 3. S ⊃ T / ~ R 4. R ⊃ T 2, 3, HS 5. ~ R 1, 4, MT

Correct

For each of the following proofs, either the justification for a derived line has been omitted or else the derivation has been omitted. Choose the correct answer for each question. 1. ~ C v ( ~ B ⊃ D ) 2. ~ B 3. ~ C ⊃ B / D v E 4. 2, 3, MT 5. ~ B ⊃ D 6. 2, 5, MP 7. D v E The derivation in line 6 is:

D

"Every horse has four legs. Samson has a horse. Therefore, Samson's horse has four legs." This argument is: deductive or inductive

Deductive

There has been an overall decrease in violence among humans worldwide throughout recorded history. Biologically speaking, this is because the genetic characteristics for nonviolence have been selected over time by the species. This is an example of: argument or explanation

Explaination

A counterexample to an argument is evidence that the conclusion is false.

False

A self-contradiction is a statement that is sometimes true.

False

A simple statement requires at least one logical operator.

False

A single counterexample to an inductive argument is enough to show that an argument is invalid.

False

A tautology is a statement that is sometimes false.

False

When premises are dependent, the truth of any one is sufficient to justify the conclusion.

False

"Building fuel-efficient cars helps reduce gasoline consumption. Dependency on foreign oil for gasoline production is a drain on the economy. Offshore oil drilling is dangerous. Oil spills through faulty drilling are hazardous to life; so are large tanker spills. Carbon emissions are hurting the environment. We need to start building more fuel-efficient cars" In this argument, "Building fuel-efficient cars helps reduce gasoline consumption" is: premise or conculsion

Premise

"Hamburgers are loaded with saturated fat and sodium. Pizza is loaded with saturated fat and sodium. Too much saturated fat and sodium is harmful to your heart. Jim takes in too much saturated fat and sodium. It follows that Jim is harming his heart." Here, "Too much saturated fat and sodium is harmful to your heart" is: premise or conculsion

Premise

The last line of each example gives the reference to the line or lines needed for its derivation. You are to determine the correct rule of inference. 1. ( ~ S v ~ R ) · ~ M 2. ~ S v ~ R 1, ___

Simp

The last line of each example gives the reference to the line or lines needed for its derivation. You are to determine the correct rule of inference. Reference: Ref 8-1 1. ( ~ S v ~ R ) · ~ M 2. ~ S v ~ R 1, ___

Simp

The vast majority of students who don't have a book for the course, and who don't do the homework, wind up failing the course. I know for a fact that Michael doesn't have a book and he doesn't do the homework. Michael will fail the course. The argument above is: strong or weak

Strong

A compound statement has at least one simple statements as a component.

True

A truth table is an arrangement of truth values for a compound proposition that displays for every possible case how the truth value of the proposition is determined by the truth values of its simple components.

True

A valid argument can be an unsound argument.

True

An inclusive disjunction is where both disjuncts can be true at the same time.

True

In ordinary language the words "only if" typically precedes the consequent of a conditional statement.

True

The function of the rules of inference is to justify the steps of a proof.

True

Use your knowledge of conjunction, disjunction, negation and truth tables to determine whether the following arguments are valid or invalid. Note on identifying the premises and conclusions in these kinds of questions: Premise 1 is the first line (I ⊃ ~ C); Premise 2 is just below it (C); and the Conclusion is always after the the forward slash (~ I ) I ⊃ ~ C C / ~ I

Valid

Use your knowledge of conjunction, disjunction, negation and truth tables to determine whether the following arguments are valid or invalid. (Note: There is only one premise in this argument. The conclusion is after the forward slash, P) ( ~ R · ~ S ) ⊃ P / P

Valid

The exam's range of C scores is 70-79. I got a C on the exam. Therefore, maybe I got a 75 on the exam. The inductive argument above is: strong or weak

Weak

For each of the following proofs, either the justification for a derived line has been omitted or else the derivation has been omitted. Choose the correct answer for each question. Proof 9 1. ~ C v ( ~ B ⊃ D ) 2. ~ B 3. ~ C ⊃ B / D v E 4. 2, 3, MT 5. ~ B ⊃ D 6. 2, 5, MP 7. D v E The derivation in line 4 is:

???

The last line of each example gives the reference to the line or lines needed for its derivation. You are to determine the correct rule of inference. 1. (T v S) v R 2. ~P 3. [(T v S) v R] · ~ P 1, 2, ___

???

Only a few people will be chosen for the Olympic team. Of those receiving phone calls from the selection committee, 20% will make the team. John received a phone call from the selection committee. John will probably make the Olympic team. The argument above is: strong or weak

Weak