For questions 1–6, Part A is asking you to partially translate the argument by making the proper substitutions. Part B is asking you to choose which substitution results in a counterexample, thus invalidating the argument.Base your answers to questions 7–11 on Categorical Proposition 1A: "All wiretaps that are approved without a warrant are surveillance techniques that are not legal."For questions 12–16, select the correct answer for each multiple choice question.For questions 17–19 you are given a statement, its truth value in parentheses, and an operation or relation to be performed on that statement. You must identify the new statement and the truth value of the new statement. Base your response on the classical square of opposition.Base your answers to questions 20–22 on Syllogistic Form 1A given below:Some M are not P.No S are M.Some S are not P.Base your answers to questions 23–25 on Syllogistic Form 6A given below:No P are M.Some S are M.Some S are not P.For questions 26–30, select the correct translation for each problem.Base your answers to questions 31–32 on Proposition 1A, given below:  Base your answers to questions 33–34 on Proposition 2A, given below:  For the given statement, use an ordinary truth table to answer the question that follows.Statement 1A(N → K) ↔ (K → N) 
Question1
PARTASomecashmere sweaters are fashionable garments, so some cashmere sweatersare not suede jackets, for some suede jackets are not fashionablegarments. Which of the following correctly expressesthe form of this argument?
Some C are F.Some C are not S.Some S are not F. 

Some S are not F.Some C are F.Some C are not S. 

Some C are not F.Some C are not S.Some C are F. 

Some F are not S.Some F are C.Some S are not C. 

Some C are F.Some F are not S.Some S are not S. 
Question2
PARTBSomecashmere sweaters are fashionable garments, so some cashmere sweatersare not suede jackets, for some suede jackets are not fashionablegarments. Which of the following substitutionsproves the argument invalid?
C = animals, F = cats, S = mammals. 

C = dogs, F = animals, S = mammals. 

C = dogs, F = mammals, S = fish. 

C = mammals, F = animals, S = dogs. 

C = cats, F = mammals, S = animals. 
Question3
PARTBIfcell phone companies screen text messages, then freedom of speech isthreatened. Thus, freedom of speech is not threatened, because cellphone companies do not screen text messages. Whichof the following substitutions proves the argument invalid?
C = Abraham Lincoln was assassinated, F = George Washington was assassinated. 

C = Joe Smith was beheaded, F = Joe Smith is dead. 

C = Abraham Lincoln was beheaded, F = Abraham Lincoln is dead. 

C = Abraham Lincoln was assassinated, F = Abraham Lincoln is dead. 

C = Abraham Lincoln was beheaded, F = Abraham Lincoln is not dead. 
Question4
PARTAIfcell phone companies screen text messages, then freedom of speech isthreatened. Thus, freedom of speech is not threatened, because cellphone companies do not screen text messages. Whichof the following correctly expresses the form of this argument?
If C then F.C.            F. 

Not F. Not C.       If C then F. 

All C are F. C.            F. 

If C then F. Not C.      Not F. 

If C then F. Not F.      Not C. 
Question5
PARTAAllcontainer ships that are oceangoing are air polluters. Hence, allcontainer ships are air polluters. Which of thefollowing correctly expresses the form of this argument?
All C are A.All C are O. 

All C are A.              All C that are O are A. 

All CS are O.All CS are A. 

All C are O.All C are A. 

All C that are O are A.All C are A. 
Question6
PARTBAllcontainer ships that are oceangoing are air polluters. Hence, allcontainer ships are air polluters. Which of thefollowing substitutions proves the argument invalid?
C = husbands, O = married, A = men. 

C = men, O = humans, A = mammals. 

C = men, O = married, A = husbands. 

C = wives, O = divorced, A = women. 

C = cats, O = animals, A = dogs. 
Question7
InCategorical Proposition 1A, the subject term is:
Surveillance techniques that are not legal. 

Warrant 

Surveillance techniques. 

Wiretaps. 

Wiretaps that are approved without a warrant. 
Question8
InCategorical Proposition 1A, the copula is:
Are. 

Are not. 

All. 

Affirmative. 

Are not legal. 
Question9
InCategorical Proposition 1A, the quantifier is:
Are. 

Particular. 

All. 

Universal. 

Are not. 
Question10
InCategorical Proposition 1A, the quality is:
Not. 

Universal. 

Negative. 

Affirmative. 

Particular. 
Question11
InCategorical Proposition 1A:
The subject term is universal and the predicate term is particular. 

The subject term is distributed and the predicate term is undistributed. 

The subject term is undistributed and the predicate term is distributed. 

Both the subject term and the predicate term are distributed. 

Both the subject term and the predicate term are undistributed. 
Question12
Whichof the following categorical propositions is in standard form?
No mutual funds are completely without risk. 

No physicians are immune from making mistakes. 

Not every restaurant serves organic food. 

Some carwashes are solarpowered operations. 

All sleep aids are not drugs without side effects. 
Question13
Theproposition "No flight delays are occurrences welcomed bypassengers" is an:
Itype. 

Utype. 

Etype. 

Otype. 

Atype. 
Question14
Giventhe categorical proposition "Some teaching careers are notrewarding occupations." If the quality but not the quantity ischanged, the resulting proposition is:
Some teaching careers are rewarding occupations. 

All teaching careers are unrewarding occupations. 

No teaching careers are rewarding occupations. 

All teaching careers are rewarding occupations. 

Some teaching careers are unrewarding occupations. 
Question15
Giventhe categorical proposition "No corporations are real persons."If the quantity but not the quality is changed, the resultingproposition is:
No real persons are corporations. 

Some corporations are not real persons. 

All corporations are real persons. 

Some corporations are real persons. 

No corporations are not real persons. 
Question16
Giventhe categorical proposition "All Emmy winners are celebrities."If both the quality and the quantity are changed, the resultingproposition is:
No Emmy winners are people who are not celebrities. 

All people who are not celebrities are people who are not Emmy winners. 

No Emmy winners are celebrities. 

Some Emmy winners are celebrities. 

Some Emmy winners are not celebrities. 
Question17
AllA are B. (T)        Contrary
No A are B. (Und.) 

All B are A. (Und.) 

Some A are B. (T) 

No A are B. (F) 

No A are nonB. (T) 
Question18
SomeA are not nonB. (F)      Contradiction
Some A are nonB. (T) 

All A are nonB. (T) 

Some B are not nonA. (F) 

Some A are nonB. (T) 

Some A are B. (T) 
Question19
SomenonA are not B. (T)      Subcontrary
Some nonA are B. (Und.) 

No nonA are B. (Und.) 

All nonA are B. (F) 

Some A are B. (T) 

Some nonB are not A. (T) 
Question20
ForSyllogistic Form 1A, after filling in the Venn diagram,
Areas 2 and 3 are shaded, and there is an X on the line between areas 1 and 4. 

Areas 5 and 6 are shaded, and there is an X on the line between areas 1 and 2. 

Areas 2 and 3 are shaded, and there is an X in area 1. 

Areas 1 and 2 are shaded, and there is an X in area 3. 

Areas 1 and 2 are shaded, and there is an X in area 3. 
Question21
ForSyllogistic Form 1A, the mood and figure is:
EAE4 

IEI1 

OEO3 

OAO2 

OEO1 
Question22
ForSyllogistic Form 1A, the argument is:
Invalid, exclusive premises. 

Invalid, illicit major. 

Invalid, undistributed middle. 

Valid, no fallacy. 

Invalid, drawing an affirmative conclusion from negative premises. 
Question23
ForSyllogistic Form 6A, after filling in the Venn diagram,
Areas 3 and 4 are shaded, and there is an X in area 5. 

Areas 3 and 4 are shaded, and there is an X in area 2. 

Areas 3, 4, 5, and 6 are shaded. 

Areas 5 and 6 are shaded, and there is an X on the line between areas 3 and 4. 

Areas 6 and 7 are shaded, and there is an X on the line between areas 2 and 3. 

Question 24 For Syllogistic Form 6A, the mood and figure is:
Question 25 For Syllogistic Form 6A, the answer from the Boolean standpoint is:
Question 26 Either Breitling has a diamond model and Rado advertises a calendar watch or Tissot has luminous hands.
Question 27 If Movado offers a blue dial, then neither Fossil is water resistant nor Nautica promotes a titanium case.
Piaget has a gold watch only if both Seiko has leather bands and Breitling has a diamond model. Gucci features stainless steel also, Fossil is water resistant given that Cartier offers a stop watch.
Movado and Nautica offer a black dial if and only if Piaget has a gold watch.
Given that A and B are true and X and Y are false, determine the truth value of Proposition 1A.  True  False In Proposition 1A, the main operator is a:
Given that A and B are true and X and Y are false, determine the truth value of Proposition 2A.  True  False In Proposition 2A, the main operator is a:
Question 35 Statement 1A is:
Question 36 Statement 2A is:

Question37
Giventhe pair of statements, use truth tables to determine theirrelationship:
 Thesestatements are:
Logically equivalent. 

Valid. 

Contradictory. 

Consistent. 

Inconsistent. 
Question38
H→ ~MM        ~H
Denying the Antecedent (DA)—invalid. 

Modus Ponens (MP)—valid. 

Affirming the Consequent (AC)—invalid. 

Modus Tollens (MT)—valid. 

Hypothetical Syllogism (HS)—valid. 
Question39
~D→ N  D      ~N
MP—valid. 

MT—invalid. 

DA—invalid. 

AC—invalid. 

Invalid. 
Question40
~S~S → F F
MP—valid. 

AC—valid. 

MT—valid. 

AC—invalid. 

Disjunctive Syllogism (DS)—valid. 
Question41
Sv ~TS      ~T
DA—invalid. 

Constructive Dilema (CD)—valid. 

Invalid. 

Destructive Dilema (DD)—valid. 

CD—invalid. 
Completethe truth table to show whether the following argument is valid orinvalid. If the argument is invalid, you must specify acounterexample.
Premise1: J → (K→ L)Premise 2: K → (J → L)Conclusion: (Jv K) → L
J 
K 
L 
J   →   (K → L) 
K →  (J → L) 
(J   v   K)  →  L 
 T 
 T 
 T 
 T 
 T 
 T 
 T 
 T 
 F 
 T 
 T 
 T 
 T 
 F 
 T 
 F 
 F 
 T 
 F 
 T 
 T 
 F 
 F 
 F 
 F 
 F 
 F 
 F 
 F 
 F 
 F 
 F 
 T 
 T 
 F 
 F 
 F 
 T 
 F 
 T 
 F 
 F 
 T 
 F 
 F 
 T 
 T 
 T 
Question43
Proofby Natural Deduction – Propositional Logic. Use a direct proof toshow that the following argument is valid.
Premise1: (E • I) v (M •U)Premise 2: ~EConclusion: ~(E v ~M)
Question44
Proofby Natural Deduction – Predicate Logic. Use a direct proof to showthat the following argument is valid.Premise1:  Premise2:  Conclusion: 
(Lx• Mx)v(~Lx•~Mx) –hypothesis
LetQ= Lx, R =Mx
2.(Q v (~Q•~R))•(R v (~Q•~R))—distributivity of v
3.(Q v ~Q)•(Q v~R)•(R v~Q)•(R v~R)–distributivity of v
4.T•(Q v~R)•(R v~Q)•T —tautology
5.T•(Q v~R)•(R v~Q) —idempotency of T
6.(Q v~R)•(R v~Q) simplification
7.(R > Q)•(Q > R) material implication
8.Q = R tautology
9.N>~ (Q=R) —hypothesis
10.(Q=R) > ~N contrapositive of #9
11.~Kc modus ponens from #8 and #10
12.Mc v Kc hypothesis
13.Mc disjunctive syllogism fr