Question 1
A biconditional statement whose main components are consistentstatements 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 equivalentstatements 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 isfalse that,” and “n’t.”
3 points
Question 4
A conditional statement where both the antecedent and consequentare 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 ofthe following statement.
If the shoe fits, then one has to wear it.
3 points
Question 6
Identify which of the following is a correct symbolization ofthe following statement.
If you say it cannot be done, youshould 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 mainconnective 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 mainconnective should be:
3 points
Question 10
In the truth table for the statement form p •q, the column of truth values underneath the mainconnective 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 fiveequivalence rules DM, Contra, Imp, Bicon, Exp. Identify therule.
~(R ? U) ? ~(T ? O)
~[(R ? U) • (T ? O)]
3 points
Question 15
The following argument is an instance of one of the fiveequivalence rules DM, Contra, Imp, Bicon, Exp. Identify therule.
~S ? ~(~G ? U)
(~G ? U) ? S
3 points
Question 16
The following argument is an instance of one of the fiveequivalence rules Taut, DN, Com, Assoc, Dist. Identify therule.
(G ? R) • (E ? S)
[(G ? R) • E] ? [(G ? R) • S]
3 points
Question 17
The following argument is an instance of one of the fiveequivalence rules Taut, DN, Com, Assoc, Dist. Identify therule.
(~N ? D) ? (T • K)
[(~N ? D) ? T] • [(~N ? D) ? K)
3 points
Question 18
The following argument is an instance of one of the fiveequivalence rules Taut, DN, Com, Assoc, Dist. Identify therule.
~W • O
~~~W • O
3 points
Question 19
The following argument is an instance of one of the fiveinference forms MP, MT, HS, DS, Conj. Identify the form.
[(G • R) ? (S ? P)] ? (N • G)
~(N • G)
~[(G • R) ? (S ? P)]
3 points
Question 20
The following argument is an instance of one of the fiveinference forms MP, MT, HS, DS, Conj. Identify the form.
M ? O
(M ? O) ? (F • R)
F • R
3 points
Question 21
The following argument is an instance of one of the fiveinference 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]
3 points
Question 22
The following argument is an instance of one of the fiveinference forms MP, MT, HS, DS, Conj. Identify the form.
T ? H
~H
T
3 points
Question 23
The following argument is an instance of one of the fiveinference forms MP, MT, HS, DS, Conj. Identify the form.
(K ? N) ? (O • W)
~(O • W)
(K ? N)
3 points
Question 24
The following argument is an instance of one of the fiveinference forms Simp, Conj, Add, CD, DD. Identify the form.
M • S
M
M • (M • S)
3 points
Question 25
The following argument is an instance of one of the fiveinference forms Simp, Conj, Add, CD, DD. Identify the form.
(X ? M) • (R ? A)
X ? R
M ? A
3 points
Question 26
The following argument is an instance of one of the fiveinference forms Simp, Conj, Add, CD, DD. Identify the form.
(P ? R) • (V ? V)
~R ? ~V
~P ? ~V
3 points
Question 27
The following argument is an instance of one of the fiveinference forms Simp, Conj, Add, CD, DD. Identify the form.
[(~S ? U) ? (T ? E)] • [(D ? E) ?~N]
(~S ? U) ? (D ? E)
(T ? E) ? ~N
3 points
Question 28
The following argument is an instance of one of the fiveinference forms Simp, Conj, Add, CD, DD. Identify the form.
[(S ? P) ? (C ? I)] • [(F ? ~C) ?M]
(S ? P) ? (F ? ~C)
(C ? I) ? M
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 sentencesshows 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 sentencesshows 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 sentencesshows 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 sentencesshows 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 sentencesshows 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, ifany, set of truth values assigned to the atomic sentences showsthat 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, ifany, set of truth values assigned to the atomic sentences showsthat 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, ifany, set of truth values assigned to the atomic sentences showsthat 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
3 points
Question 42
Which rule is used in the following inference?
F ? G
~A ? (F ? G)
3 points
Question 43
Which rule is used in the following inference?
L • ~F
~F
3 points
Question 44
Which rule is used in the following inference?
E • (F ? G)
H ? (F • G)
[E • (F ? G)] • [H ? (F • G)]
3 points
Question 45
Which rule is used in the following inference?
~(R ? S) ? [~O • (P ? Q )]
~(R ? S) ? [~O • (~~P ? Q )]
3 points
Question 46
Which rule is used in the following inference?
(M ? N) ? (~L • K)
[(M ? N) ? ~L] • [(M ? N) ? K]
3 points
Question 47
Which rule is used in the following inference?
M
M ? N
3 points
Question 48
Which, if any, of the following proofs are correctdemonstrations 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 areincomplete. |
3 points
Question 49
Which, if any, of the following proofs are correctdemonstrations 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 areincomplete. |
| | Neither proof |
3 points
Question 50
Which, if any, of the following proofs are correctdemonstrations 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 areincomplete. |
3 points
