Question 1 A biconditional statement whose main components are consistent statem

ID: 3194888 • Letter: Q

Question

Question 1

A biconditional statement whose main components are consistent statements is itself a:

coherency

contingency

self-contradiction

unable to determine from the information given

tautology

3 points

Question 2

A biconditional statement whose main components are equivalent statements is itself a:

self-contradiction

coherency

unable to determine from the information given

contingency

tautology

3 points

Question 3

Choose which symbol to use for “it is not the case that,” “it is false that,” and “n’t.”

•

3 points

Question 4

A conditional statement where both the antecedent and consequent are equivalent statements is itself a:

unable to determine from the information given

tautology

coherency

contingency

self-contradiction

3 points

Question 5

Identify which of the following is a correct symbolization of the following statement.
If the shoe fits, then one has to wear it.

F • W

F W

3 points

Question 6

Identify which of the following is a correct symbolization of the following statement.
If you say it cannot be done, you should not interrupt the one doing it.

~S ~I

~S • ~I

S ~I

~S ~I

3 points

Question 7

Identify the main connective in the following statement.

L [(W L) ~(Y T)]

•

3 points

Question 8

In the truth table for the statement form ~(p p), the column of truth values underneath the main connective should be FF. Therefore, this statement form is a:

contingency

contradiction

tautology

equivalency

self-contradiction

3 points

Question 9

In the truth table for the statement form p q, the column of truth values underneath the main connective should be:

TFFF

TFFT

TTTF

TTFF

TFTT

3 points

Question 10

In the truth table for the statement form p • q, the column of truth values underneath the main connective should be TFFF. Therefore, this statement form is a:

tautology

contingency

contradiction

equivalency

self-contradiction

3 points

Question 11

Symbolize “both not p and not q.”

~( p • q)

~p • q

( p q) • (~p q)

( p q) • ~( p • q)

~p • ~q

3 points

Question 12

The connective used for biconditionals is:

•

3 points

Question 13

The statement form p q is:

not actually a statement form

a conjunction

a conditional

a disjunction

a biconditional

3 points

Question 14

The following argument is an instance of one of the five equivalence rules DM, Contra, Imp, Bicon, Exp. Identify the rule.
~(R U) ~(T O)
~[(R U) • (T O)]

Bicon

Exp

Contra

Imp

3 points

Question 15

The following argument is an instance of one of the five equivalence rules DM, Contra, Imp, Bicon, Exp. Identify the rule.
~S ~(~G U)
(~G U) S

Bicon

Exp

Imp

Contra

3 points

Question 16

The following argument is an instance of one of the five equivalence rules Taut, DN, Com, Assoc, Dist. Identify the rule.
(G R) • (E S)
[(G R) • E] [(G R) • S]

Com

Assoc

Dist

Taut

3 points

Question 17

The following argument is an instance of one of the five equivalence rules Taut, DN, Com, Assoc, Dist. Identify the rule.
(~N D) (T • K)
[(~N D) T] • [(~N D) K)

Assoc

Dist

Taut

Com

3 points

Question 18

The following argument is an instance of one of the five equivalence rules Taut, DN, Com, Assoc, Dist. Identify the rule.
~W • O
~~~W • O

Com

Assoc

Taut

Dist

3 points

Question 19

The following argument is an instance of one of the five inference forms MP, MT, HS, DS, Conj. Identify the form.
      [(G • R) (S P)] (N • G)
      ~(N • G)
      ~[(G • R) (S P)]

Conj

3 points

Question 20

The following argument is an instance of one of the five inference forms MP, MT, HS, DS, Conj. Identify the form.
      M O
      (M O) (F • R)
      F • R

Conj

3 points

Question 21

The following argument is an instance of one of the five inference forms MP, MT, HS, DS, Conj. Identify the form.
      [(P T) • (H • N)] (T ~S)
      (T ~S) [(H E) R]
      [(P T) • (H • N)] [(H E) R]

Conj

3 points

Question 22

The following argument is an instance of one of the five inference forms MP, MT, HS, DS, Conj. Identify the form.
T H
~H
T

Conj

3 points

Question 23

The following argument is an instance of one of the five inference forms MP, MT, HS, DS, Conj. Identify the form.
      (K N) (O • W)
      ~(O • W)
      (K N)

Conj

3 points

Question 24

The following argument is an instance of one of the five inference forms Simp, Conj, Add, CD, DD. Identify the form.
M • S
M
M • (M • S)

Add

Simp

Conj

3 points

Question 25

The following argument is an instance of one of the five inference forms Simp, Conj, Add, CD, DD. Identify the form.
      (X M) • (R A)
      X R
      M A

Conj

Add

Simp

3 points

Question 26

The following argument is an instance of one of the five inference forms Simp, Conj, Add, CD, DD. Identify the form.
      (P R) • (V V)
      ~R ~V
      ~P ~V

Simp

Add

Conj

3 points

Question 27

The following argument is an instance of one of the five inference forms Simp, Conj, Add, CD, DD. Identify the form.
      [(~S U) (T E)] • [(D E) ~N]
      (~S U) (D E)
      (T E) ~N

Simp

Add

Conj

3 points

Question 28

The following argument is an instance of one of the five inference forms Simp, Conj, Add, CD, DD. Identify the form.
      [(S P) (C I)] • [(F ~C) M]
      (S P) (F ~C)
      (C I) M

Simp

Add

Conj

3 points

Question 29

Use a short form truth table to answer the following question. Which, if any, set of truth values assigned to the atomic sentences shows that the following argument is invalid?
A (J S)
~J
S
A

None—the argument is valid.

A: F J: F S: T

A: T J: F S: T

A: T J: T S: F

A: T J: T S: T

3 points

Question 30

Use a short form truth table to answer the following question. Which, if any, set of truth values assigned to the atomic sentences shows that the following argument is invalid?
(E • ~H) G
~(H G)
~E

None—the argument is valid.

E: T H: F G: T

E: T H: T G: F

E: F H: F G: F

E: T H: T G: T

3 points

Question 31

Use a short form truth table to answer the following question. Which, if any, set of truth values assigned to the atomic sentences shows that the following argument is invalid?
      (Z Y) X
      Z W
      ~Y ~W
      V W

Z: F Y: F X: T W: F V: F

Z: F Y: F X: F W: F V: F

Z: T Y: T X: T W: T V: T

None—the argument is valid.

Z: T Y: T X: F W: F V: F

3 points

Question 32

Use a short form truth table to answer the following question. Which, if any, set of truth values assigned to the atomic sentences shows that the following argument is invalid?
S R
~D
S D
~R

S: F R: F D: F

S: T R: T D: F

S: F R: T D: F

None—the argument is valid.

S: T R: T D: T

3 points

Question 33

Use a short form truth table to answer the following question. Which, if any, set of truth values assigned to the atomic sentences shows that the following argument is invalid?
      (B • C) F
      (F • E) (J • P)
      (B • C) P

B: F C: T F: T E: F J: F P: F

B: T C: T F: T E: F J: T P: F

None—the argument is valid.

B: F C: F F: F E: F J: F P: F

B: T C: T F: T E: T J: T P: F

3 points

Question 34

Use a truth table to answer the following question. Which, if any, set of truth values assigned to the atomic sentences shows that the following argument is invalid?
A B
A
~B

A: T B: T

A: F B: F

A: F B: T

None—the argument is valid.

A: T B: F

3 points

Question 35

Use a truth table to answer the following question. Which, if any, set of truth values assigned to the atomic sentences shows that the following argument is invalid?
~(P • I)
~P ~I

P: T I: F

P: F I: F

None—the argument is valid.

P: T I: T

P: F I: T

3 points

Question 36

Use a truth table to answer the following question. Which, if any, set of truth values assigned to the atomic sentences shows that the following argument is invalid?
C • E
E • C

C: T E: T

C: F E: F

C: F E: T

None—the argument is valid.

C: T E: F

3 points

Question 37

Which rule is used in the following inference?
      (D ~E) F
      F (G • H)
      (D ~E) (G • H)

3 points

Question 38

Which rule is used in the following inference?
      (A • B) (C D)
      A • B
      C D

3 points

Question 39

Which rule is used in the following inference?
      [(A B) (C B)] ~(~A • ~C)
      (A B) (C B)
      ~(~A • ~C)

3 points

Question 40

Which rule is used in the following inference?
      ~(F • K) (F L)
      ~(F L)
      ~~(F • K)

3 points

Question 41

Which rule is used in the following inference?
(B • C) D
~D
B • C

Conj

Add

Simp

3 points

Question 42

Which rule is used in the following inference?
F G
~A (F G)

Add

Simp

Conj

3 points

Question 43

Which rule is used in the following inference?
L • ~F
~F

Conj

Add

Simp

3 points

Question 44

Which rule is used in the following inference?
      E • (F G)
      H (F • G)
      [E • (F G)] • [H (F • G)]

Conj

Simp

Add

3 points

Question 45

Which rule is used in the following inference?
~(R S) [~O • (P Q )]
~(R S) [~O • (~~P Q )]

Assoc

Com

Dist

Taut

3 points

Question 46

Which rule is used in the following inference?
(M N) (~L • K)
[(M N) ~L] • [(M N) K]

Dist

Assoc

Taut

Com

3 points

Question 47

Which rule is used in the following inference?
M
M N

Conj

Simp

Add

3 points

Question 48

Which, if any, of the following proofs are correct demonstrations of the validity of this argument?
      (P • Q ) • (R S)
Q
      Proof 1
(1) (P • Q ) • (R S)      /Q      Premise/Conclusion
(2) P • Q            1 Simp
(3) R S            1 Simp
(4) P                  2 Simp
(5) Q            2 Simp
      Proof 2
(1) (P • Q ) • (R S)      /Q      Premise/Conclusion
(2) P • Q            1 Simp
(3) Q            2 Simp

Proof 2

Proof 1

Proofs 1 and 2

Neither proof

Not enough information is provided because proofs are incomplete.

3 points

Question 49

Which, if any, of the following proofs are correct demonstrations of the validity of this argument?
      (P R) C
      C ~R
      Proof 1
(1) (P R) C      /C ~R      Premise/Conclusion
(2) ~(P R) C            1 Imp
(3) (~P • ~R) C            2 DM
(4) C (~P • ~R)            3 Com
(5) (C ~P) • (C ~R)            4 Dist
(6) C ~R            5 Simp
      Proof 2
(1) (P R) C      /C ~R      Premise/Conclusion
(2) ~(P R) C            1 Imp
(3) (~P • ~R) C            2 DM
(4) (~P C) • (~R C)            3 Dist
(5) ~R C            4 Simp
(6) C ~R            5 Com

Proof 1

Proofs 1 and 2

Proof 2

Not enough information is provided because proofs are incomplete.

Neither proof

3 points

Question 50

Which, if any, of the following proofs are correct demonstrations of the validity of this argument?
      A (B C)
      B (~C ~A)
      Proof 1
(1) A (B C)      /B (~C ~A)      Premise/Conclusion
(2) (A • B) C      1 Exp
(3) (B • A) C      2 Com
(4) B (A C)      3 Exp
(5) B (~C ~A)      4 Contra
      Proof 2
(1) A (B C)      /B (~C ~A)      Premise/Conclusion
            (2) B      Assumption
            (3) A      Assumption
            (4) B C      1, 3 MP
            (5) C      2, 4 MP
            (6) A C      3–5 CP
(7) B (A C)      2–6 CP
(8) B (~C ~A)      7 Contra

Proofs 1 and 2

Proof 1

Neither proof

Proof 2

Not enough information is provided because proofs are incomplete.

3 points

coherency

contingency

self-contradiction

unable to determine from the information given

tautology

Explanation / Answer

1. contingency

2. tautology

3. negation (option 1)

4. tautology

5.F W (because to wear a shoe it must fit in first hence fitting in is a subset of wearing)

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