exam 6 phil
Pick the best definition of Tautology in SL A sentence that is true for all truth-value assignments. A sentence A for which ⊨ A in all models. A sentence that is true for some variable assignment in every model. A and B are a tautology if A ⊨ B and B ⊨ A. None of these is correct
A sentence that is true for all truth-value assignments.
Pick the best definition of Logically Equivalent in QL A set of sentences are logically equivalent in QL if and only if there is at least one model in which all of the sentences are true. A set of sentences are logically equivalent in QL if and only if there is no model in which the premises are true but the conclusion is false. A set of sentences are logically equivalent in QL if and only if there is no model where one of the sentences is true and the others are false. A set of sentences are logically equivalent in QL if and only in every model where one sentence is true, the others are also true, and for every model where one sentence is false, the others are also false. It is not possible to define logical equivalence in QL.
A set of sentences are logically equivalent in QL if and only in every model where one sentence is true, the others are also true, and for every model where one sentence is false, the others are also false.
Pick the best definition of Consistent in QL It is not possible to define consistency in QL. A set of sentences is consistent in QL if and only if there is at least one variable assignment for which all of the sentences are satisfied. A set of sentences is consistent in QL if and only if there is no model where one of the sentences is true and the rest are false. A set of sentences is consistent in QL if and only if there is at least one model in which all of the sentences are true. None of the above.
A set of sentences is consistent in QL if and only if there is at least one model in which all of the sentences are true.
Pick the best definition of Logically Equivalent in SL A set of sentences is logically equivalent if and only if there is at least one truth-value assignment where all of the sentences are true. A set of sentences is logically equivalent if and only if the sentences all have the same truth value on each truth-value assignment; if one of the sentences is true, the others are true, and if one of them is false, all of them are false. A set of sentences is logically equivalent if and only if each of the sentences has the same truth value on any truth-value assignment; if the sentence is true on one truth-value assignment, it is true on every other assignment. There is at least one model where all of the sentences in the set are true. None of these is correct.
A set of sentences is logically equivalent if and only if the sentences all have the same truth value on each truth-value assignment; if one of the sentences is true, the others are true, and if one of them is false, all of them are false.
Pick the best definition of Valid in SL A. On any truth value assignment where the premises are true, the conclusion must also be true. B. There is at least one truth-value assignment where all the sentences in the set are true. C. The premises and the conclusion are true in every model. D. On every truth-value assignment where the conclusion is false, all of the premises are false. E. (A) and (D)
A. On any truth value assignment where the premises are true, the conclusion must also be true.
Pick the best definition of Semantic entailment (⊨) in SL {A1, A2, A3, ...} ⊨ B if and only if there is no truth-value assignment for which all of the sentences in the set {A1, A2, A3, ...} are true but B is false. All of the above. None of the above.
All of the above.
Pick the best definition of Valid in QL An argument where {P1, P2, ...} ⊨ Cfor all truth value assignments. An argument is valid in QL if and only if there is no model in which the premises are true but the conclusion is false. An argument is valid in QL if and only if there is at least one model where the premises are truth and the conclusion is true. An argument is valid in QL only if it is true in every model. None of the above.
An argument is valid in QL if and only if there is no model in which the premises are true but the conclusion is false.
Pick the best definition of Invalid in QL An argument where, relative to some model, the premises are true, but the conclusion is false. An argument where there is no model where the premises are true and the conclusion is true. An argument that is false on every truth-value assignment. An argument such that there is no model where one of the sentences is true and the rest are false. None of these is correct.
An argument where, relative to some model, the premises are true, but the conclusion is false
Define the following in terms of semantic entailment: Logically Equivalent ⊨ A and ⊨ B B ⊨ A and A ⊨ B A ⊨ B It is not possible to define logical equivalence using semantic entailment. None of these is correct.
B ⊨ A and A ⊨ B
Finally, suppose you meet a pair named Jonn and Betti. Betti asked Jonn, "Are you the type who could ask whether at least one of us is of type B?" What types would you think they are? Both are B. There's not enough information to answer this question.
Both are B.
Suppose, instead, ze had asked you whether ze is of type A. What would you have concluded? Ze is of type A. Ze is of type B. Neither type could ask that question. Both types could ask that question.
Both types could ask that question.
Use models to determine whether the following sentence is a tautology, contradiction, or contingent:∀x[(Lxy&Lyx)↔︎x=y] Tautology Contradiction Contingent
Contingent
Use models to determine whether the following sentence is a tautology, contradiction, or contingent:∃xPx Tautology Contradiction Contingent
Contingent
Define the following in terms of semantic entailment: A is a Tautology B. A is always semantically entailed. C. There is some B such that B⊨A D. (A) and (B) E. None of these is correct.
D. (A) and (B)
Hs→∃xCx True False
FALSE
∀x∀y[(Mxy∨Myx)↔︎(Fx&Fy)] True False
FALSE
∀x∃y[(Lxy∨Lyx)&x=y] True False
FALSE
Using models, determine whether the following argument in QL is valid or invalid: ∃x(Ax&Bx)∃x¬Ax∃x¬Bx∴ ∃x(¬Ax&¬Bx) Valid Invalid
INVALID
using models, determine whether the following argument in QL is valid or invalid: ∀x(Ax→Bx)∀x(Ax→Cx)∴ ∀x(Bx→Cx) Valid Invalid
INVALID
Suppose you met a couple on the planet named Kay and Tracey, and Kay asked Tracey, "Darling, are we of different types?" What types would you think they are? Both are B. Kay could be either, but Tracey is B. Tracey could be either, but Kay is A.
Kay could be either, but Tracey is B.
Using models, determine which of the following applies to this set of sentences in QL:{ ∀x(Ax&¬Ax), [(Ma∨Qb)&(¬Ma&¬Qb)], (∀xTx&∃x¬Tx) } Logically equivalent and inconsistent Not logically equivalent, but consistent Not logically equivalent and inconsistent.
Logically equivalent and inconsistent
Using models, determine which of the following applies to this set of sentences in QL:{∀x(Ax→Bx), ∀x(Bx→Cx), ∃x(Ax&¬Cx)} Not logically equivalent and inconsistent.
Not logically equivalent and inconsistent.
Using models, determine which of the following applies to this set of sentences in QL:{(Ma∨Mb), ¬(Ma&Mb), ¬Mb} Logically equivalent and consistent Not logically equivalent, but consistent Not logically equivalent and inconsistent.
Not logically equivalent, but consistent
Using models, determine which of the following applies to this set of sentences in QL:{∀x(Ax→Bx), ∀x(Bx→Cx), ∃x(¬Ax&Cx)} Not logically equivalent, but consistent
Not logically equivalent, but consistent
Cs→∀x(Fx↔︎Hx) True False
TRUE
d=w True False
TRUE
∀x x=x True False
TRUE
∀x[Hx→∃y(Lxy)] True False
TRUE
∀x∃y(Lxy∨Lyx) True False
TRUE
∃x(Cx∨(Fx&Hx)) True False
TRUE
if your symbolization key for QL says that your "UD: letters and numbers in 'PHIL 2303'," how would you best represent the universe of discourse in a model? UD = {PHIL 2303} UD = {P, H, I, L, 2, 3, 0} UD = {P, H, L, 2, 3, 0}
UD = {P, H, I, L, 2, 3, 0}
Using models, determine whether the following argument in QL is valid or invalid: ∀x(Ax→Bx)∀x(Bx→Cx)∃x¬Cx∴ ∃x¬Ax Valid Invalid
VALID
Using models, determine whether the following argument in QL is valid or invalid: ∀x[(Ax&Bx)→Cx]∃x(Bx&¬Cx)∴ ∃x¬Cx Valid Invalid
VALID
Which truth value assignment makes the following statement of SL true?(A&¬B) a(A)=1, a(B)=1 a(A)=1, a(B)=0 a(A)=0, a(B)=1 a(A)=0, a(B)=0 None of the above
a(A)=1, a(B)=0
Which truth value assignment makes the following statement of SL false?(X→Y)&(Y→X) a(X)=0, a(Y)=0 All of the above None of the above
a(X)=1, a(Y)=0
Using models, determine whether the following argument in QL is valid or invalid: ∃x(Ax&Bx)∃x(¬Ax&¬Bx)∴ ∀x(Ax↔︎Bx) Valid Invalid
invalid
