3. Sophia - Critical Thinking - Unit 3

Question 4 Mark this question Consider the following natural language sentence:Customers with a membership card always receive a discount. Which answer is a translation of this natural language sentence into formal logic? M = A customer has a membership card.D = The customer receives a discount.M → D M = A customer has a membership card.D = The customer receives a discount.M ∧ D M = A customer has a membership card.D = The customer receives a discount.M ↔ D D = The customer receives a discount.M = A customer has a membership card.D → M

M = A customer has a membership card.D = The customer receives a discount.M → D

Which of the following arguments is represented by the Venn diagrams below? Some A are C. Some B are A. Therefore, all B are C. All A are C. Some B are A. Therefore, all B are C. No A are C. Some B are not A. Therefore, all B are C. All A are C. Some B are not A. Therefore, no B are C.

No A are C. Some B are not A. Therefore, all B are C.

Consider the sentence below: Some S are P. Which sentence is contradictory with this sentence? All S are P. No P are S. No S are P. Some S are not P.

No S are P.

Which relation(s) does the predicate "hates" encode? Symmetrical Transitive None of these Reflexive

None of these

Consider the following proof: E E → P..∴ (P ∧ E) ∨ V Which of the following is a derivation needed for this proof? P ∨ E V P → E P

P

Consider the argument below: Cats are pets with the best personalities. Cats have the best personalities. Cats are pets. Which is the best translation of this argument? P = Cats are pets.B = Cats have the best personalities. P ↔ B B ∴P P = Cats are pets.B = Cats have the best personalities. P ∨ B B ∴P P = Cats are pets.B = Cats have the best personalities. P ∧ B B ∴P P = Cats are pets.B = Cats have the best personalities. P → B B ∴P

P = Cats are pets.B = Cats have the best personalities. P ∧ B B ∴P

Consider the following: P Q..∴ (P ∧ Q) ∨ D Which of the following can be derived from the premises? D ¬D P ∧ Q P ∨ Q

P ∨ Q

What are the components of a proof? Statements in natural language Necessary, possible, and contingent truths Premises, derivations, conclusion Sentences that are shown to be sound

Premises, derivations, conclusion

Consider the following natural language sentence:Everything that rises must converge. Which answer is a translation of this natural language sentence into formal logic? R = Something is a thing that rises.C = The thing converges. R ∧ C R = Something is a thing that rises.C = The thing converges. R ∨ C R = Something is a thing that rises.C = The thing converges. R → C C = The thing converges.R = Something is a thing that rises. C → R

R = Something is a thing that rises.C = The thing converges. R → C

Consider the following natural language sentence:You can't have any candy unless you clean your room. Which answer is a translation of this natural language sentence into formal logic? R = You clean your room.C = You have candy.¬R ∧ C R = You clean your room.C = You have candy.¬R ∧ ¬C R = You clean your room.C = You have candy.¬R → C R = You clean your room.C = You have candy.¬R → ¬C

R = You clean your room.C = You have candy.¬R → ¬C

Consider the following natural language sentence: You can have steak or fish for dinner. Which answer is an "exclusive or" translation of this natural language sentence? S = You can have steak.F = You can have fish. S ∨ F ∧ ¬S ∧ ¬F S = You can have steak.F = You can have fish. (S ∨ F) ∧ ¬(S ∧ F) S = You can have steak.F = You can have fish. (S ∨ F) ∧ (¬S ∧ F) S = You can have steak. F = You can have fish. (S ∨ F) ∨ ¬(S ∧ F)

S = You can have steak.F = You can have fish. (S ∨ F) ∧ ¬(S ∧ F)

Consider the sentence below: No S are P. Which sentence is contradictory with this sentence? Some S are not P. No P are S. Some S are P. All S are P.

Some S are P

Which of the following arguments is represented by the Venn diagrams below? Note that the argument may or may not be valid. Premises Conclusion All S are P. Therefore, some S are not P. Some S are not P. Therefore, no S are P. Some S are not P. Therefore, all S are P. No S are P. Therefore, all S are P.

Some S are not P. Therefore, all S are P.

Question 15 Mark this question Which of the following categorical sentences is represented by the Venn diagram below? All plants eat bugs. Some plants don't eat bugs. No plants eat bugs. Some plants eat bugs.

Some plants eat bugs.

Which relation(s) does the predicate "is next to" encode? Reflexive Symmetrical Transitive All three (reflexive, symmetrical, and transitive)

Symmetrical

Which of the following is true of subproofs? They help us justify the conclusion. They are the rules of logic. They justify the premises in a proof. They justify the rules of logic.

They help us justify the conclusion

What is the purpose of using a propositional variable? To represent any proposition, not a specific one To represent a specific proposition, not any one To represent a person's name To represent the name of a place

To represent any proposition, not a specific one

Consider the following: U ∧ F U → B..∴B Which of the following can be derived from the premises? F ¬(U ∧ F) ¬U U

U

Consider the following natural language sentence: You can use my car if you ever need it. Which answer is a translation of this natural language sentence into formal logic? U = You can use my car.N = You need my car. N ∨ U U = You can use my car.N = You need my car. N ∴ U U = You can use my car.N = You need my car. N → U U = You can use my car.N = You need my car. U → N

U = You can use my car.N = You need my car. N → U

Consider the following symbol: ∨ What is the meaning of this symbol? conditional conjunction negation disjunction

disjunction

Consider the following: F → (B ∨ A) D → F ¬(B ∨ A)..∴ ¬(D ∧ C) Which of the following can be derived from the premises? ¬(D ∨ C) ¬B ¬B ∨ ¬A ¬D

¬D

What are the two equivalent translations of a "neither...nor" statement? ¬p ∨ ¬q¬ (p ∧ q) ¬p ∧ ¬q¬ (p ∨ q) p ∨ q¬ p → q ¬p ∧ ¬q¬ p → ¬q

¬p ∧ ¬q¬ (p ∨ q)

Consider the following proof: ¬(L → M) → N M v N ¬N..∴ L → M Which of the following is a derivation needed for this proof? ¬¬(L → M) N ¬¬¬N M

¬¬(L → M)

Which of the following statements is a tautology? (p ∧ ¬p) ↔ (q ∨ ¬q) (p ∧ ¬p) ↔ ¬(q ∨ ¬q) (p ∧ ¬p) → ¬(q ∨ q) (p ↔ ¬p) ∧ (q ∨ ¬q)

(p ∧ ¬p) ↔ ¬(q ∨ ¬q)

Which of the following statements is a contingency? (p ∨ ¬p) → (¬p → q) (p ↔ ¬p) ∧ (q ∨ ¬q) (p ∧ ¬p) ↔ ¬(q ∨ ¬q) (p ∧ ¬p) → ¬(q ∨ ¬q)

(p ∨ ¬p) → (¬p → q)

Which of the following statements is a contingency? (¬p → q) → (p ∧ q) (p ↔ ¬p) ∧ (q ∨ ¬q) (p ∧ ¬p) → ¬(q ∨ ¬q) (p ∧ ¬p) ↔ ¬(q ∨ ¬q)

(¬p → q) → (p ∧ q)

Consider the following natural language sentence: Neither acid rain nor a lightning storm can keep us from camping this weekend. Which answer is a translation of this natural language sentence into formal logic? A = Acid rain keeps us from camping.L = A lightning storm keeps us from camping. ¬A ∧ L A = Acid rain keeps us from camping.L = A lightning storm keeps us from camping. ¬(A ∧ L) A = Acid rain keeps us from camping.L = A lightning storm keeps us from camping. ¬A ∨ ¬L A = Acid rain will keep us from camping.L = A lightning storm will keep us from camping. ¬A ∧ ¬L

A = Acid rain will keep us from camping.L = A lightning storm will keep us from camping. ¬A ∧ ¬L

Which of the following is true of proofs? A proof demonstrates validity through application of inference rules. They consist only of rules of inference that demonstrate validity. A proof uses intuition alone to demonstrate the validity of an argument. Because they involve more steps, they are more complicated to construct than truth tables.

A proof demonstrates validity through application of inference rules.

Which of the following statements is a tautology? A.) (p ∧ ¬p) → ¬(q ∨ ¬q) B.) ¬(p ∧ q) → ¬(p ∨ q) C.) (p ∧ ¬p) ↔ (q ∨ ¬q) D.) (p ↔ ¬p) ∧ (q ∨ ¬q)

A.) (p ∧ ¬p) → ¬(q ∨ ¬q)

Consider the following sentence: Some S are not P. Which sentence is not compatible with this sentence? A.) All S are P. B.) No S are P. C.) No P are S. D.) Some P are S.

A.) All S are P.

Consider the argument below: Unless you brush your teeth, you can't have candy. You didn't brush your teeth. No candy for you. Which is the best translation of this argument? A.) B = You brush your teeth.C = You have candy. ¬B → ¬C ¬B ∴¬C B.) B = You brush your teeth.C = You have candy. B → ¬C ¬B ∴¬C C.) B = You brush your teeth.C = You have candy. ¬B → C ¬B ∴C D.) B = You brush your teeth.C = You have candy. ¬B ∨ ¬C ¬B ∴¬C

A.) B = You brush your teeth.C = You have candy. ¬B → ¬C ¬B ∴¬C

Consider the following natural language sentence: You can have broccoli or spinach for dinner but not both. Which answer is a translation of this natural language sentence into formal logic? A.) B = You can have broccoli.S = You can have spinach. (B ∨ S) ∧ ¬(B ∧ S) B.) B = You can have broccoli.S = You can have spinach. B ∨ S ∧ ¬B ∧ S C.) B = You can have broccoli.S = You can have spinach. ¬B ∧ S D.) B = You can have broccoli.S = You can have spinach. B ↔ S

A.) B = You can have broccoli.S = You can have spinach. (B ∨ S) ∧ ¬(B ∧ S)

Consider the following argument: p → q p ∴q Which rule of inference was used to derive the conclusion in this argument? A.) Conditional Elimination B.) Hypothetical Syllogism C.) Conditional Introduction D.) Modus Tollens

A.) Conditional Elimination

Consider the following argument: ¬(p ∧ q) ∴¬p ∨ ¬q Which rule of inference was used to derive the conclusion in this argument? A.) DeMorgan's Laws B.) Disjunctive Syllogism C.) Conjunction Introduction D.) Conjunction Elimination

A.) DeMorgan's Laws

Consider the following natural language sentence: Sal doesn't like green hats. Which answer is a translation of this natural language sentence into formal logic? A.) G = Sal likes green hats. ¬G B.) G = Sal doesn't like green hats. ¬G C.) G = Sal likes green hats. ∧G D.) G = Sal doesn't like green hats. G

A.) G = Sal likes green hats. ¬G

Consider the following: K → (Q ∨ X) (Q ∨ X) → R Q..∴ ¬U ∨ (K → R) Which of the following is a next step working up from the conclusion? A.) K → R B.) ¬U ∨ (K → R) C.) Q ∨ X D.) ¬U

A.) K → R

Which of the following categorical sentences is represented by the Venn diagram below? A.) No humans live on Mars. B.) Some humans don't live on Mars. C.) All humans live on Mars. D.) Some humans live on Mars.

A.) No humans live on Mars.

Consider the following natural language sentence:I'll go hiking tomorrow unless it rains. Which answer is a translation of this natural language sentence into formal logic? A.) R = It rains tomorrow.H = I go hiking tomorrow.¬R → H B.) H = I go hiking tomorrow.R = It rains tomorrow.H → ¬R C.) R = It rains tomorrow.H = I go hiking tomorrow.R → H D.) R = It doesn't rain tomorrow.H = I go hiking tomorrow.R → H

A.) R = It rains tomorrow.H = I go hiking tomorrow.¬R → H

Consider the sentence below: Some S are P. Which sentence is entailed by this sentence? A.) Some P are S. B.) All P are S. C.) All S are P. D.) No S are P.

A.) Some P are S.

Consider the following sentence: All S are P. If we know this sentence is true, which other sentence must be false? A.) Some S are not P. B.) Some S are P. C.) No S are P. D.) All P are S.

A.) Some S are not P.

What is the purpose of using constants? A.) To represent a specific proposition B.) To represent a person's name C.) To represent the name of a place D.) To represent a general proposition

A.) To represent a specific proposition

Which sentence is materially equivalent to ¬p ∧ ¬q? A.) ¬(p ∨ q) B.) ¬(p ∧ q) C.) p → q D.) ¬p ∨ ¬q

A.) ¬(p ∨ q)

Which argument can be represented by the following Venn diagrams? A.)No A are B. No B are C. Therefore, no A are C. B.)No A are B. All B are C. Therefore, No A are C C.)All A are B. All B are C. Therefore, all A are C. D.)All A are B. Some B are C. Therefore, some A are C.

A.)No A are B. No B are C. Therefore, no A are C.

Which of the following arguments is represented by the Venn diagrams below? All C are A. All A are B. Some B are C. All C are A. Some A are B. Some B are C. Some C are A. Some A are B. Some B are C. All C are A. No A are B. Some B are not C.

All C are A. Some A are B. Some B are C.

Which of the following categorical sentences is represented by the Venn diagram below? No children listen to their parents. Some children don't listen to their parents. All children listen to their parents. Some children listen to their parents.

All children listen to their parents.

Which relation(s) does the predicate "is the same as" encode? Transitive Reflexive All three (reflexive, symmetrical, and transitive) Symmetrical

All three (reflexive, symmetrical, and transitive)

Consider the argument below: Either the butler or the maid did it. The butler's prints were on the knife. The prints wouldn't be on the knife unless he used it. If the butler used the knife, then he must have done it! So, the butler did it. Which is the best translation of this argument? B = The butler did it.M = The maid did it.P = The butler's prints were on the knife.U = The butler used the knife. B ∨ M P U → P U → B ∴B B = The butler did it.M = The maid did it.P = The butler's prints were on the knife.U = The butler used the knife. B ∨ M P ¬U → ¬P U → B ∴B B = The butler did it.M = The maid did it.P = The butler's prints were on the knife.U = The butler used the knife. B ∨ M P U → ¬P U → B ∴B B = The butler did it.M = The maid did it.P = The butler's prints were on the knife.U = The butler used the knife. B ∨ M P ¬U → P U → B ∴B

B = The butler did it.M = The maid did it.P = The butler's prints were on the knife.U = The butler used the knife. B ∨ M P ¬U → ¬P U → B ∴B

Consider the following natural language sentence: You'll never get bored at the beach. Which answer is a translation of this natural language sentence into formal logic? B = It's not the case that you'll sometimes get bored at the beach. ¬B B = You'll never get bored at the beach. B B = You'll sometimes get bored at the beach. ¬B B = You'll never get bored at the beach. ¬B

B = You'll sometimes get bored at the beach. ¬B

Which of the following statements is a contradiction? A.) ¬(p ∧ q) → ¬(p ∨ q) B.) (p ∧ ¬p) ↔ (q ∨ ¬q) C.) (p ∧ ¬p) → ¬(q ∨ ¬q) D.) (p ∧ ¬p) ↔ ¬(q ∨ ¬q)

B.) (p ∧ ¬p) ↔ (q ∨ ¬q)

Which of the following statements is a contingency? A.) (p ∧ ¬p) → ¬(q ∨ ¬q) B.) (p ∨ ¬q) → (¬p → q) C.) (p ↔ ¬p) ∧ (q ∨ ¬q) D.) (p ∧ ¬p) ↔ (q ∨ ¬q)

B.) (p ∨ ¬q) → (¬p → q)

Which of the following is true of proofs? A.) A proof is a sentence whose truth we have derived. B.) A proof is a way to show why an argument is valid. C.) A proof is a sentence whose truth we take for granted. D.) A proof is a way to show that an argument is true.

B.) A proof is a way to show why an argument is valid.

Which of the following categorical sentences is represented by the Venn diagram below? A.) Some cats are cute. B.) All cats are cute. C.) No cats are cute. D.) Some cats aren't cute.

B.) All cats are cute.

Consider the following argument: p → q ¬q ∴¬p Which rule of inference was used to derive the conclusion in this argument? A.) Conditional Elimination B.) Modus Tollens C.) Modus Ponens D.) Conditional Introduction

B.) Modus Tollens

Consider the following natural language sentence:Every oyster has a pearl. Which answer is a translation of this natural language sentence into formal logic? A.) O = A thing is an oyster.P = The thing has a pearl. O ∧ P B.) O = A thing is an oyster.P = The thing has a pearl. O → P C.) O = A thing is an oyster.P = The thing has a pearl. P → O D.) O = A thing is an oyster.P = The thing has a pearl. O ∨ P

B.) O = A thing is an oyster.P = The thing has a pearl. O → P

Which of the following categorical sentences is represented by the Venn diagram below? A.) All gators dwell on land. B.) Some gators dwell on land. C.) No gators dwell on land. D.) Some gators don't dwell on land.

B.) Some gators dwell on land.

Consider the argument below: If you wake up early, you can catch the sunrise. You don't catch the sunrise. So, you didn't wake up early. Which is the best translation of this argument? A.) W = You wake up early.S = You catch the sunrise. W ↔ S ¬S ∴¬W B.) W = You wake up early.S = You catch the sunrise. W → S ¬S ∴¬W C.) W = You wake up early.S = You catch the sunrise. W ∧ S ¬S ∴¬W D.) W = You wake up early.S = You catch the sunrise. W → S S ∴¬W

B.) W = You wake up early.S = You catch the sunrise. W → S ¬S

Consider the following natural language sentence: You're either with us or you're against us, but not both. Which answer is a translation of this natural language sentence into formal logic? A.) W = You're with us.A = You're against us. (W ∧ A) ∧ ¬(W ∨ A) B.) W = You're with us.A = You're against us. (W ∨ A) ∧ ¬(W ∧ A) C.) W = You're with us.A = You're against us. W ∨ A ∧ ¬(W ∧ A) D.) W = You're with us.A = You're against us. (W ∨ A) ∧ (¬W ∧ A)

B.) W = You're with us.A = You're against us. (W ∨ A) ∧ ¬(W ∧ A)

Consider the following: (¬Z ∨ ¬I) → ¬(H ∧ Q) (¬H ∨ ¬Q) → (L → Y) ¬Z...∴(L → Y) Which of the following can be derived from the premises? A.) ¬(H ∨ Q) B.) ¬Z ∨ ¬I C.) L D.) ¬I

B.) ¬Z ∨ ¬I

Consider the argument below: Dogs are neither cute nor mischievous. Dogs are actually cute. Thus, dogs are not mischievous. Keeping in mind that the argument is invalid, which is the best translation of this argument? C = Dogs are cute.M = Dogs are mischievous. ¬C ∧ ¬M C ∴¬M C = Dogs are cute.M = Dogs are mischievous. ¬(C ∨ M) ¬C ∴ M C = Dogs are cute.M = Dogs are mischievous. ¬(C ∧ M) ¬C ∴ M C = Dogs are not cute.M = Dogs are not mischievous. C ∨ M ¬C ∴ M

C = Dogs are cute.M = Dogs are mischievous. ¬C ∧ ¬M C ∴¬M

Consider the following natural language sentence: Although you like cookies, eating too many is bad for your health. Which answer is a translation of this natural language sentence into formal logic? C = You like eating cookies.B = Eating too many cookies is bad for your health. C ¬ B C = You like eating cookies.B = Eating too many cookies is bad for your health. C ∧ B C = You like eating cookies.B = Eating too many cookies is bad for your health. C → B C = You like eating cookies.B = Eating too many cookies is bad for your health. C ∨ B

C = You like eating cookies.B = Eating too many cookies is bad for your health. C ∧ B

Consider the following proof:. (¬M ∧ ¬C) → ¬(H ∨ D) (¬H ∧ ¬D) → (P → Y)...∴¬(M ∨ C) → (P → Y) Which of the following is a derivation needed for this proof? A.) ¬(M ∨ C) B.) (¬H ∧ ¬D) → (P → Y) C.) (¬M ∧ ¬C) → (P → Y) D.) P → Y

C.) (¬M ∧ ¬C) → (P → Y)

Consider the following natural language sentence: I'm neither angry nor upset. Which answer is a translation of this natural language sentence into formal logic? A.) A = I'm not angry.U = I'm not upset. ¬A ∨ ¬U B.) A = I'm angry.U = I'm upset. ¬(A ∧ U) C.) A = I'm angry. U = I'm upset. ¬(A ∨ U) D.) A = I'm angry.U = I'm upset. ¬A ∨ ¬U

C.) A = I'm angry. U = I'm upset. ¬(A ∨ U)

Which answer is the "inclusive or" translation of this natural language sentence? A.) L = I love you.H = I hate you. (L ∨ H) ∧ (L ∧ H) B.) L = I love you.H = I hate you. L ∧ H C.) L = I love you.H = I hate you. L ∨ H D.) L = I love you.H = I hate you. (L ∨ H) ∧ ¬(L ∧ H)

C.) A = I'm angry. U = I'm upset. ¬(A ∨ U)

Consider the following: (B ∨ C) → ¬F B..∴ ¬F Which of the following can be derived from the premises? A.) F B.) B C.) B ∨ C D.) C

C.) B ∨ C

Consider the argument below: You can have cake or brownies. Actually, we don't have any brownies. So, you can have cake. Which is the best translation of this argument? A.) C = You can have cake.B = You can have brownies C ∧ B ¬C ∴B B.) C = You can have cake.B = You can have brownies. C ∧ B ¬B ∴C C.) C = You can have cake.B = You can have brownies. C ∨ B ¬B ∴C D.) C = You can have cake.B = You can have brownies. C ∨ B ¬B ∧ C ∴C

C.) C = You can have cake.B = You can have brownies. C ∨ B

Consider the following argument: p ∧ q ∴p Which rule of inference was used to derive the conclusion in this argument? A.) Disjunctive Syllogism B.) Conjunction Introduction C.) Conjunction Elimination D.) Disjunction Introduction

C.) Conjunction Elimination

Consider the following natural language sentence: We can go to dinner or the movies. Which answer is a translation of this natural language sentence into formal logic? A.) M = We can go to dinner or we can go to the movies. M B.) D = We can go to dinner. M = We can go to the movies. D → M C.) D = We can go to dinner. M = We can go to the movies. D ∨ M D.) D = We can go to dinner. M = We can go to the movies. D ∧ M

C.) D = We can go to dinner. M = We can go to the movies. D ∨ M

Consider the following: A ∧ C B..∴ (A ∧ C) ∧ (D ∨ B) Which of the following is a next step working up from the conclusion? A.) B B.) A ∧ C C.) D ∨ B D.) D ∧ B

C.) D ∨ B

Consider the following natural language sentence: Sal loves eating cookies but hates cake. Which answer is a translation of this natural language sentence into formal logic? A.) L = Sal loves eating cookies.H = Sal hates cake. L ∨ H B.) L = Sal loves eating cookies.H = Sal hates cake. L ¬ H C.) L = Sal loves eating cookies.H = Sal hates cake. L ∧ H D.) L = Sal loves eating cookies.H = Sal hates cake. L → H

C.) L = Sal loves eating cookies.H = Sal hates cake. L ∧ H

Consider the following natural language sentence: Nobody loves mac and cheese more than me. Which answer is a translation of this natural language sentence into formal logic? A.) M = Nobody loves mac and cheese more than me. M B.) M = Everybody loves mac and cheese more than me. ¬M C.) M = Somebody loves mac and cheese more than me. ¬M D.) M = Somebody doesn't love mac and cheese more than me. ¬M

C.) M = Somebody loves mac and cheese more than me. ¬M

Which statement regarding the comparison between proofs and truth tables is true? A.) Truth tables explain validity, but proofs do not. B.) Proofs are more tedious to construct. C.) Proofs are more efficient and powerful. D.) Truth tables are more powerful and efficient.

C.) Proofs are more efficient and powerful.

Consider the following natural language sentence:If you see a penny, pick it up, all day long you'll have good luck. Which answer is a translation of this natural language sentence into formal logic? A.) S = You see a penny, pick it up.G = All day long you'll have good luck.G → S B.) S = You see a penny.P = You pick the penny up.G = All day long you'll have good luck.(S → P) → G C.) S = You see a penny.P = You pick the penny up.G = All day long you'll have good luck.(S ∧ P) → G D.) S = You see a penny, pick it up.G = All day long you'll have good luck.S → G

C.) S = You see a penny.P = You pick the penny up.G = All day long you'll have good luck.(S ∧ P) → G

Which relation(s) does the predicate "is a co-worker of" encode? A.) Reflexive and transitive B.) Symmetrical and reflexive C.) Symmetrical and transitive D.) Symmetrical, transitive and reflexive

C.) Symmetrical and transitive

Which relation(s) does the predicate "is taller than" encode? A.) Symmetrical B.) None of these C.) Transitive D.) Reflexive

C.) Transitive

Consider the following: ¬(V ∧ W) → (C ∧ F) ¬C ∨ ¬F..∴V Which of the following can be derived from the premises? A.) C ∧ F B.) ¬(V ∧ W) C.) V ∧ W D.) ¬C ∨ ¬F

C.) V ∧ W

Which argument is represented by the following Venn diagrams? A.)Some A are not B. No B are C. Therefore, no A are C. B.)All A are B. All B are C. Therefore, some A are not C. C.)Some A are C. All A are B. Therefore, no A are C. D.)Some A are C. All B are B. Therefore, all A are C.

C.)Some A are C. All A are B. Therefore, no A are C.

Consider the following argument: p ∴p ∨ q Which rule of inference was used to derive the conclusion in this argument? Conjunction Introduction Disjunction Introduction Disjunctive Syllogism DeMorgan's Laws

Conditional Elimination

Consider the following argument: Z → (M ∧ F) (M ∧ F) → (H ∨ ¬P) ∴ Z → (H ∨ ¬P) Which rule of inference was used to derive the conclusion in this argument? Conditional Introduction Modus Tollens Conditional Elimination Modus Ponens

Conditional Introduction

Consider the following argument: p q ∴p ∧ q Which rule of inference was used to derive the conclusion in this argument? Conjunction Introduction Conjunction Elimination Disjunction Introduction Disjunctive Syllogism

Conjunction Introduction

Consider the following argument: All men are mortal. Socrates is a man. Therefore, Socrates is mortal. Which rule of inference was used to derive the conclusion in this argument? Conditional Introduction Modus Ponens Modus Tollens Conditional Elimination

Consider the following natural language sentence: Jan doesn't go to school. Which answer is a translation of this natural language sentence into formal logic? S = Jan goes to school. ¬S S = Jan doesn't go to school. ¬S S = Jan goes to school. ∴S S = Jan doesn't go to school. ∴S

Consider the following natural language sentence: Pineapple is a delicious fruit. Which answer is a translation of this natural language sentence into formal logic? D = Pineapple is delicious.F = Pineapple is a fruit. D ↔ F D = Pineapple is delicious.F = Pineapple is a fruit. D ∧ F D = Pineapple is delicious.F = Pineapple is a fruit. D ∨ F D = Pineapple is delicious.F = Pineapple is a fruit. D → F

D = Pineapple is delicious.F = Pineapple is a fruit. D ∧ F

Consider the following natural language sentence:You can have dessert if and only if you finish your dinner. Which answer is a translation of this natural language sentence into formal logic? D = You have dessert.F = You finish dinner.D ↔ F D = You have dessert.F = You finish dinner.F ∧ D D = You have dessert.F = You finish dinner.F → D D = You have dessert.F = You finish dinner.D → F

D = You have dessert.F = You finish dinner.D ↔ F

Which sentence is p ↔ q equivalent to? A.) (p ∧ q) ↔ (q ∧ p) B.) (p ↔ q) ∧ (q ↔ p) C.) (p ∧ q) → (q ∧ p) D.) (p → q) ∧ (q → p)

D.) (p → q) ∧ (q → p)

What are rules of inference? A.) A set of rules that tells us how to make an argument in natural language B.) A set of rules that tells us how to write a proof C.) A set of rules that tells us how to think in everyday arguments D.) A set of rules that tells us what sentences follow from what sentences

D.) A set of rules that tells us what sentences follow from what sentences

Consider the following argument: p → q q → r ∴p → r Which rule of inference was used to derive the conclusion in this argument? A.) Modus Ponens B.) Modus Tollens C.) Conditional Elimination D.) Conditional Introduction

D.) Conditional Introduction

Consider the following argument: p ∨ q ¬q ∴ p Which rule of inference was used to derive the conclusion in this argument? A.) Conjunction Introduction B.) Disjunction Introduction C.) Conjunction Elimination D.) Disjunctive Syllogism

D.) Disjunctive Syllogism

Consider the following natural language sentence:All roads lead to Rome. Which answer is a translation of this natural language sentence into formal logic? A.) R = A thing is a road.L = The thing leads to Rome.L → R B.) R = A thing is a road.L = The thing leads to Rome.L ∨ R C.) R = A thing is a road.L = The thing leads to Rome.R ∧ L D.) R = A thing is a road.L = The thing leads to Rome.R → L

D.) R = A thing is a road.L = The thing leads to Rome.R → L

symmetry, reflexivity, and transitivity. Which relation(s) does the predicate "is a sister of" encode? A.) Symmetrical and reflexive B.) Reflexive and transitive C.) All three (reflexive, symmetrical, and transitive) D.) Transitive only

D.) Transitive only

Consider the following natural language sentence: Uli brought wine to the party, but I brought nothing because I forgot. Which answer is a translation of this natural language sentence into formal logic? A.) U = Uli brought wine. I = I brought something. F = I forgot. U ∧ ¬(I ∧ F) B.) U = Uli brought wine. I = I brought something. F = I forgot. U ∧ ¬I ∧ F C.) U = Uli brought wine. I = I brought something. F = I forgot. (U ∧ ¬I) ∧ F D.) U = Uli brought wine. I = I brought something. F = I forgot. U ∧ (¬I ∧ F)

D.) U = Uli brought wine. I = I brought something. F = I forgot. U ∧ (¬I ∧ F)

Consider the following symbol: ∧ What is the meaning of this symbol? A.) conditional B.) disjunction C.) negation D.) conjunction

D.) conjunction

Which of the following symbols is used for conditional statements? A.) ¬ B.) ∨ C.) ∧ D.) →

D.) →

Which argument can be represented by the following Venn diagrams? Premises Conclusion A.)No S are P.Therefore, all P are S. B.)No S are P. Therefore, some S are P. C.)Some S are P.Therefore, all S are P. D.)All S are P.Therefore, some S are not P.

D.)All S are P.Therefore, some S are not P.

Consider the following argument: ¬p ∨ ¬q ∴¬(p ∧ q) Which rule of inference was used to derive the conclusion in this argument? Conjunction Elimination Disjunctive Syllogism Conjunction Introduction DeMorgan's Laws

DeMorgan's Laws

Consider the following argument: (D → L) → (G → S) D → L ∴ G → S Which rule of inference was used to derive the conclusion in this argument? Modus Tollens Conditional Elimination Hypothetical Syllogism Conditional Introduction

Hypothetical Syllogism

Consider the following natural language sentence: Hal loved the boy who played with dolls. Which answer is a translation of this natural language sentence into formal logic? L = Hal loved the boy. H = The boy played with dolls. L ∨ H L = Hal loved the boy who played with dolls. L L = Hal loved the boy. H = The boy played with dolls. L ∧ H L = Hal loved the boy. H = The boy played with dolls. L → H

L = Hal loved the boy. H = The boy played with dolls. L ∧ H