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
		F
		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
		~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
		DM
		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
		DM
		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
		DN
		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
		DN

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

		DN
		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)]

		HS
		MT
		Conj
		DS
		MP

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

		MT
		DS
		MP
		HS
		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]

		MP
		DS
		Conj
		MT
		HS

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

		MT
		DS
		HS
		Conj
		MP

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)

		HS
		Conj
		DS
		MT
		MP

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
		DD
		CD

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

		DD
		Conj
		Add
		CD
		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

		CD
		DD
		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

		DD
		Simp
		Add
		Conj
		CD

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
		CD
		DD
		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)

		MT
		DD
		HS
		CD
		MP

3 points

Question 38

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

		HS
		DD
		CD
		MT
		MP

3 points

Question 39

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

		MP
		MT
		HS
		DD
		CD

3 points

Question 40

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

		CD
		MP
		MT
		HS
		DD

3 points

Question 41

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

		Conj
		Add
		Simp
		HS
		DS

3 points

Question 42

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

		Add
		Simp
		HS
		DS
		Conj

3 points

Question 43

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

		Conj
		DS
		HS
		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
		DS
		HS
		Simp
		Add

3 points

Question 45

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

		DN
		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
		DN

3 points

Question 47

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

		Conj
		DS
		HS
		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

Answer 1

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

Correct answer is a contingency

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

Correct answer is tautology

Question 3

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

		~
		•
		≡
		∨
		⊃

3 points

Correct option is (first option)

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

It is a tautology as A will always imply A