Question 1

Translate each of the following sentences into predicate logic, using the given constants and predicates.
-Neither Gabriel nor Honoré play volleyball. (g: Gabriel; h: Honoré; Vx: x plays volleyball)

Accepted Answer

The answer of Translate each of the following sentences into...

Question 2

1. (∃x)(Hx • ∼Ix)
2. (∀x)(Hx ⊃ Jx)
3. ∼(∃x)(Jx • Kx)
-Which of the following propositions is derivable from the given premises in M?

Accepted Answer

A)  (∃x)Ix 
B)  (∀x)∼(Ix $ \lor $ Kx) 
C)  (∃x) ∼Hx 
D)  (∀x)∼(Ix • Kx) 
E)  (∃x)∼(Ix $ \lor $ Kx)

Question 3

select the best translation into predicate logic.
-No apriorist rationalists are skeptics, but Hume is.

Accepted Answer

A)  (∀x)[(Ax • Rx) ⊃ Sx] • Sh 
B)  (∀x)[(Ax • Rx) ⊃ ∼Sx] • Sh 
C)  ∼(∀x)[(Ax • Rx) ⊃ Sx] • Sh 
D)  ∼(∀x)[(Ax • Rx) ⊃ ∼Sx] • Sh

Question 4

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates.
-Kyrone has a thriving practice if Jalissa stops touring.

Accepted Answer

A)  Tj ⊃ Pk 
B)  Tj $ \lor $ Pk 
C)  Tj ⊃ ∼Pk 
D)  ∼Kp ⊃ Jt 
E)  Jt ≡ Kp

Question 5

use: t: Tortuga
Bx: x creates bricks 
Cx: x is a city
Nx: x is nicely placed 
Px: x is productive 
Sx: x is a settlement
Tx: x has a trading port 
Wx: x is on the water
-All cities are productive if and only if they are both nicely placed and not on the water.

Accepted Answer

The answer of use: t: Tortuga
Bx: x creates bricks 
Cx:...

Question 6

derive the conclusions of each of the following arguments using the rules of inference for M. Do not use conditional or indirect proof.
-1. (∀x)(Jx ⊃ Kx)
2. ∼(∀x)Kx / ∼(∀x)Jx

Accepted Answer

The answer of derive the conclusions of each of the...

Question 7

Translate each sentence into predicate logic, using the given translation keys.
Ax: x is an athlete
Dx: x has determination
Px: x plays professional sports 
Sx: x receives a scholarship 
Tx: x is tall
Wx: x works hard
-Tall athletes with determination either receive scholarships or play professional sports.

Accepted Answer

The answer of Translate each sentence into predicate logic, using...

Question 8

determine whether the given formula is a logical truth of M or not. If it is not a logical truth, select a false valuation.
-[(∀x)(Fx ⊃ Gx) • (∀x)(Gx ⊃ Hx)] ⊃ (∃x)(Fx • Hx)

Accepted Answer

A)  Logical truth 
B)  Not a logical truth. False valuation in a domain of 1 member, in which: Fa: False Ga: False Ha: False 
C)  Not a logical truth. False valuation in a domain of 1 member, in which: Fa: True Ga: True Ha: False 
D)  Not a logical truth. False valuation in a domain of 1 member, in which: Fa: True Ga: True Ha: True 
E)  Not a logical truth. False valuation in a domain of 1 member, in which: Fa: True Ga: False Ha: True

Question 9

determine whether the given argument is valid or invalid. If it is valid, provide a derivation of the conclusion from the premises. If it is invalid, provide a counterexample.
-1. (∃x)(Px • Qx)
2. (∃x)(Px • Rx)
3. (∀x)(Qx ⊃ Sx)
4. (∀x)(Rx ⊃ Tx) / (∃x)(Px • Sx) • (∃x)(Px • Tx)

Accepted Answer

The answer of determine whether the given argument is valid...

Question 10

select a counterexample for the given invalid argument.
-1. (∀x)(Kx ⊃ ∼Lx)
2) (∃x)(Mx • Lx) / (∀x)(Kx ⊃ ∼Mx)

Accepted Answer

A)  Counterexample in a domain of 2 members, in which: Ka: True La: True Ma: True
Kb: True Lb: False Mb: True 
B)  Counterexample in a domain of 2 members, in which: Ka: False La: True Ma: True
Kb: True Lb: False Mb: True 
C)  Counterexample in a domain of 2 members, in which: Ka: True La: True Ma: True
Kb: True Lb: True Mb: True 
D)  Counterexample in a domain of 2 members, in which: Ka: False La: False Ma: True
Kb: True Lb: False Mb: False 
E)  Counterexample in a domain of 2 members, in which: Ka: True La: True Ma: False
Kb: True Lb: False Mb: True

Question 11

translate the given paragraphs into arguments written in M, using the given translation key. Then, derive their conclusions using the rules of inference for M.
-If some journalists are not respectable, then all journalists on the web have work to do. Some journalists on the web lack assignments. It is not the case that something without an assignment has work to do. So all journalists are respectable. (Ax: x has an assignment; Ix: x is on the web; Jx: x is a journalist; Rx: x is respectable; Wx: x has work to do)

Accepted Answer

The answer of translate the given paragraphs into arguments written...

Question 12

show that the given formula is a logical truth of M, using the rules of inference including conditional or indirect proof.
-∼(∃x)(Px • Qx) ≡ (∀x)(Px ⊃ ∼Qx)

Accepted Answer

The answer of show that the given formula is a...

Question 13

use:
b: Berkeley h: Hume
Ax: x is an apriorist 
Cx: x is consistent 
Ex: x is an empiricist 
Ix: x is an idealist 
Px: x is a person
Rx: x is a rationalist 
Sx: x is a skeptic 
Tx: x is a theist
-Only consistent rationalists are apriorists.

Accepted Answer

The answer of use:
b: Berkeley h: Hume
Ax: x is an...

Question 14

select the best translation into predicate logic.
-Some athletes play professional sports if, and only if, they have determination.

Accepted Answer

A)  (∃x)[(Ax • Px) ⊃ Dx)] 
B)  (∃x)[Dx ⊃ (Ax • Px)] 
C)  (∃x)[Ax ⊃ (Px ≡ Dx)] 
D)  (∃x)[Ax • (Px ≡ Dx)]

Question 15

select the best English interpretation of the given statements of predicate logic. 
f: Fifi
g: Gigi
Px: x is a poodle Qx: x is abused 
Rx: x is loved
Sx: x will fetch balls 
Tx: x will fetch sticks.
-(∀x){(Px • Qx) ⊃ [(Rx ⊃ (∼Sx ⊃ Tx)]}

Accepted Answer

A)  All abused poodles are loved only if they will fetch sticks and will not fetch balls. 
B)  No abused poodles will fetch sticks if they will fetch balls, and if they are loved. 
C)  All abused poodles, if they are loved, will fetch sticks if they will not fetch balls. 
D)  All abused poodles are loved if they will fetch sticks or balls. 
E)  No abused poodles will not fetch balls, if they fetch sticks and are loved.

Question 16

select a counterexample for the given invalid argument.
-1. (∀x)[Tx ⊃ (∼Wx $ \lor $ Fx)]
2) (∀x)[(∼Wx • Tx) ⊃ ∼Fx]
3) (∃x)(Tx • Fx) / (∃x)(Tx • ∼Wx)

Accepted Answer

A)  Counterexample in a domain of 1 member, in which: Ta: True Wa: False Fa: True 
B)  Counterexample in a domain of 1 member, in which: Ta: True Wa: True Fa: True 
C)  Counterexample in a domain of 1 member, in which: Ta: False Wa: True Fa: True 
D)  Counterexample in a domain of 1 member, in which: Ta: True Wa: True Fa: False 
E)  Counterexample in a domain of 1 member, in which: Ta: False Wa: True Fa: False

Question 17

select the best English interpretation of the given statements of predicate logic. 
f: Fifi
g: Gigi
Px: x is a poodle Qx: x is abused 
Rx: x is loved
Sx: x will fetch balls 
Tx: x will fetch sticks.
-(∀x)(Px ⊃ Qx) ⊃ (∃x)(Px • ∼Rx)

Accepted Answer

A)  If all poodles are abused, then some poodles are loved. 
B)  If no poodles are loved, then some poodles are abused. 
C)  If all poodles are abused, then some poodles are not loved. 
D)  If some poodles are abused, then no poodles are loved.

Question 18

Translate each of the following sentences into predicate logic, using the given constants and predicates.
-Efraim takes acting classes if, and only if, he gets time off from work. (e: Efraim; Ax: x takes acting classes; Wx: x gets time off from work)

Accepted Answer

The answer of Translate each of the following sentences into...

Question 19

Translate each of the following sentences into predicate logic, using the given constants and predicates.
-No visitor stayed for dinner. (Sx: x stayed for dinner; Vx: x is a visitor)

Accepted Answer

The answer of Translate each of the following sentences into...

Question 20

If anything is stuck in traffic, Bruno will be mad if it is late. Something is neither annoyed nor not late. If Bruno is mad, then something is annoyed. So something is not stuck in traffic.
-Which of the following is the best translation into M of this argument?

Accepted Answer

A)  $\begin{array} { l } 
( \forall \mathrm { x } ) [ \mathrm { Sx } \supset ( \mathrm { Mb } \supset \mathrm { Lx } ) ] \
( \forall \mathrm { x } ) \sim ( \mathrm { Ax } \vee \sim \mathrm { Lx } ) \
\mathrm { Mb } \supset ( \exists \mathrm { x } ) \mathrm { Ax } \quad&/(\exists x) \sim S x
\end{array}$ 
B)  $\begin{array} { l } 
( \exists \mathrm { x } ) \mathrm { Sx } \supset ( \mathrm { Mb } \supset \mathrm { Lx } ) \
( \forall \mathrm { x } ) \sim ( \mathrm { Ax } \vee \sim \mathrm { Lx } ) \
\mathrm { Mb } \supset ( \exists \mathrm { x } ) \mathrm { Ax } \quad / ( \exists \mathrm { x } ) \sim \mathrm { Sx }
\end{array}$ 
C)  $\begin{array} { l } 
( \exists \mathrm { x } ) \mathrm { Sx } \supset ( \mathrm { Lx } \supset \mathrm { Mb } ) \
( \forall \mathrm { x } ) \sim ( \mathrm { Ax } \vee \sim \mathrm { Lx } ) \
\mathrm { Mb } \supset ( \exists \mathrm { x } ) \mathrm { Ax } \quad \quad ( \exists \mathrm { x } ) \sim \mathrm { Sx }
\end{array}$ 
D)  $\begin{array} { l } 
( \forall \mathrm { x } ) [ \mathrm { Sx } \supset ( \mathrm { Lx } \supset \mathrm { Mb } ) ] \
( \forall \mathrm { x } ) \sim ( \mathrm { Ax } \vee \sim \mathrm { Lx } ) \
\mathrm { Mb } \supset ( \exists \mathrm { x } ) \mathrm { Ax } \quad \quad \quad \quad / ( \exists \mathrm { x } ) \sim \mathrm { Sx }
\end{array}$ 
E)  $\begin{array} { l } 
( \forall \mathrm { x } ) \mathrm { Sx } \supset ( \mathrm { Lx } \supset \mathrm { Mb } ) \
( \forall \mathrm { x } ) \sim ( \mathrm { Ax } \vee \sim \mathrm { Lx } ) \
\mathrm { Mb } \supset ( \exists \mathrm { x } ) \mathrm { Ax } \quad / ( \exists \mathrm { x } ) \sim \mathrm { Sx }
\end{array}$

Exam 4: Monadic Predicate Logic

Translate each of the following sentences into predicate logic, using the given constants and predicates. -Neither Gabriel nor Honoré play volleyball. (g: Gabriel; h: Honoré; Vx: x plays volleyball)

1. (∃x) (Hx • ∼Ix) 2. (∀x) (Hx ⊃ Jx) 3. ∼(∃x) (Jx • Kx) -Which of the following propositions is derivable from the given premises in M?

select the best translation into predicate logic. -No apriorist rationalists are skeptics, but Hume is.

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates. -Kyrone has a thriving practice if Jalissa stops touring.

use: t: Tortuga Bx: x creates bricks Cx: x is a city Nx: x is nicely placed Px: x is productive Sx: x is a settlement Tx: x has a trading port Wx: x is on the water -All cities are productive if and only if they are both nicely placed and not on the water.

derive the conclusions of each of the following arguments using the rules of inference for M. Do not use conditional or indirect proof. -1. (∀x)(Jx ⊃ Kx) 2. ∼(∀x)Kx / ∼(∀x)Jx

determine whether the given formula is a logical truth of M or not. If it is not a logical truth, select a false valuation. -[(∀x) (Fx ⊃ Gx) • (∀x) (Gx ⊃ Hx) ] ⊃ (∃x) (Fx • Hx)

select a counterexample for the given invalid argument. -1. (∀x) (Kx ⊃ ∼Lx) 2) (∃x) (Mx • Lx) / (∀x) (Kx ⊃ ∼Mx)

show that the given formula is a logical truth of M, using the rules of inference including conditional or indirect proof. -∼(∃x)(Px • Qx) ≡ (∀x)(Px ⊃ ∼Qx)

use: b: Berkeley h: Hume Ax: x is an apriorist Cx: x is consistent Ex: x is an empiricist Ix: x is an idealist Px: x is a person Rx: x is a rationalist Sx: x is a skeptic Tx: x is a theist -Only consistent rationalists are apriorists.

select the best translation into predicate logic. -Some athletes play professional sports if, and only if, they have determination.

select the best English interpretation of the given statements of predicate logic. f: Fifi g: Gigi Px: x is a poodle Qx: x is abused Rx: x is loved Sx: x will fetch balls Tx: x will fetch sticks. -(∀x) {(Px • Qx) ⊃ [(Rx ⊃ (∼Sx ⊃ Tx) ]}

select a counterexample for the given invalid argument. -1. (∀x) [Tx ⊃ (∼Wx $\lor$ Fx) ] 2) (∀x) [(∼Wx • Tx) ⊃ ∼Fx] 3) (∃x) (Tx • Fx) / (∃x) (Tx • ∼Wx)

select the best English interpretation of the given statements of predicate logic. f: Fifi g: Gigi Px: x is a poodle Qx: x is abused Rx: x is loved Sx: x will fetch balls Tx: x will fetch sticks. -(∀x) (Px ⊃ Qx) ⊃ (∃x) (Px • ∼Rx)

Translate each of the following sentences into predicate logic, using the given constants and predicates. -Efraim takes acting classes if, and only if, he gets time off from work. (e: Efraim; Ax: x takes acting classes; Wx: x gets time off from work)

Translate each of the following sentences into predicate logic, using the given constants and predicates. -No visitor stayed for dinner. (Sx: x stayed for dinner; Vx: x is a visitor)

If anything is stuck in traffic, Bruno will be mad if it is late. Something is neither annoyed nor not late. If Bruno is mad, then something is annoyed. So something is not stuck in traffic. -Which of the following is the best translation into M of this argument?

Exam 4: Monadic Predicate Logic

Translate each of the following sentences into predicate logic, using the given constants and predicates. -Neither Gabriel nor Honoré play volleyball. (g: Gabriel; h: Honoré; Vx: x plays volleyball)

1. (∃x) (Hx • ∼Ix) 2. (∀x) (Hx ⊃ Jx) 3. ∼(∃x) (Jx • Kx) -Which of the following propositions is derivable from the given premises in M?

select the best translation into predicate logic. -No apriorist rationalists are skeptics, but Hume is.

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates. -Kyrone has a thriving practice if Jalissa stops touring.

use: t: Tortuga Bx: x creates bricks Cx: x is a city Nx: x is nicely placed Px: x is productive Sx: x is a settlement Tx: x has a trading port Wx: x is on the water -All cities are productive if and only if they are both nicely placed and not on the water.

derive the conclusions of each of the following arguments using the rules of inference for M. Do not use conditional or indirect proof. -1. (∀x)(Jx ⊃ Kx) 2. ∼(∀x)Kx / ∼(∀x)Jx

determine whether the given formula is a logical truth of M or not. If it is not a logical truth, select a false valuation. -[(∀x) (Fx ⊃ Gx) • (∀x) (Gx ⊃ Hx) ] ⊃ (∃x) (Fx • Hx)

select a counterexample for the given invalid argument. -1. (∀x) (Kx ⊃ ∼Lx) 2) (∃x) (Mx • Lx) / (∀x) (Kx ⊃ ∼Mx)

show that the given formula is a logical truth of M, using the rules of inference including conditional or indirect proof. -∼(∃x)(Px • Qx) ≡ (∀x)(Px ⊃ ∼Qx)

use: b: Berkeley h: Hume Ax: x is an apriorist Cx: x is consistent Ex: x is an empiricist Ix: x is an idealist Px: x is a person Rx: x is a rationalist Sx: x is a skeptic Tx: x is a theist -Only consistent rationalists are apriorists.

select the best translation into predicate logic. -Some athletes play professional sports if, and only if, they have determination.

select the best English interpretation of the given statements of predicate logic. f: Fifi g: Gigi Px: x is a poodle Qx: x is abused Rx: x is loved Sx: x will fetch balls Tx: x will fetch sticks. -(∀x) {(Px • Qx) ⊃ [(Rx ⊃ (∼Sx ⊃ Tx) ]}

select a counterexample for the given invalid argument. -1. (∀x) [Tx ⊃ (∼Wx ∨ \lor ∨ Fx) ] 2) (∀x) [(∼Wx • Tx) ⊃ ∼Fx] 3) (∃x) (Tx • Fx) / (∃x) (Tx • ∼Wx)

select the best English interpretation of the given statements of predicate logic. f: Fifi g: Gigi Px: x is a poodle Qx: x is abused Rx: x is loved Sx: x will fetch balls Tx: x will fetch sticks. -(∀x) (Px ⊃ Qx) ⊃ (∃x) (Px • ∼Rx)

Translate each of the following sentences into predicate logic, using the given constants and predicates. -Efraim takes acting classes if, and only if, he gets time off from work. (e: Efraim; Ax: x takes acting classes; Wx: x gets time off from work)

Translate each of the following sentences into predicate logic, using the given constants and predicates. -No visitor stayed for dinner. (Sx: x stayed for dinner; Vx: x is a visitor)

If anything is stuck in traffic, Bruno will be mad if it is late. Something is neither annoyed nor not late. If Bruno is mad, then something is annoyed. So something is not stuck in traffic. -Which of the following is the best translation into M of this argument?

select a counterexample for the given invalid argument. -1. (∀x) [Tx ⊃ (∼Wx $\lor$ Fx) ] 2) (∀x) [(∼Wx • Tx) ⊃ ∼Fx] 3) (∃x) (Tx • Fx) / (∃x) (Tx • ∼Wx)