Question 1

derive the conclusions of each of the following arguments using the rules of inference for M, including conditional or indirect proof.
-1. (∀x)Ix $ \lor $ ∼(∃x)Hx
2. (∃x)Jx ⊃ ∼(∀x)Ix
3. Hc / (∀x)∼Jx

Accepted Answer

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

Question 2

refer to the following formula: (∃x)[Mx • (∼Nc $ \lor $ ∼Ox)] ≡ (Py • Pb)
-Which variables are bound by the '(∃x)'?

Accepted Answer

A)  The x that follows the M. 
B)  The x that follows the O. 
C)  The y that follows the P. 
D)  None of the above. 
E)  Both A and B.

Question 3

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
3. ∼(∀x)Ix $ \lor $ (∀x)Jx / (∃x)∼Ix

Accepted Answer

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

Question 4

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
-No athletes who play professional sports and have determination are neither tall nor work hard.

Accepted Answer

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

Question 5

refer to the following formula: (∃x)[(Ax • ∼Bx) • ∼(Cx $ \lor $ Dx)]
-List all of the subformulas in the scope of '(∃x)'.

Accepted Answer

The answer of refer to the following formula: (∃x)[(Ax •...

Question 6

construct a model for each of the given theories in the following domain by assigning members of the domain to the constants used in the theory and sets of members of the domain to the predicates used in the theory.
Domain = {Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune}
-(∀x)[Ax ⊃ (Bx $ \lor $ Cx)] 
Aa
Bb 
Cc

Accepted Answer

The answer of construct a model for each of the...

Question 7

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

Accepted Answer

A)  (∀x)∼Jx 
B)  (∀x)Jx 
C)  ∼(Ix • Hx) 
D)  ∼(Ix $ \lor $ Hx) 
E)  ∼(Ia $ \lor $ Hb)

Question 8

Translate each of the following sentences into predicate logic, using the given constants and predicates.
-Some visitors did not stay 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 9

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates.
-Neither Gabriel nor Honoré play volleyball.

Accepted Answer

A)  ∼(∼Vg • ∼Vh) 
B)  ∼Vg $ \lor $ ∼Vh 
C)  ∼(Vg • Vh) 
D)  ∼(Vg $ \lor $ Vh) 
E)  ∼(Vg • ∼Vh)

Question 10

construct a model for each of the given theories in the following domain by assigning members of the domain to the constants used in the theory and sets of members of the domain to the predicates used in the theory.
Domain = {Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune}
-(∃x)(Ax • ∼Bx) ⊃ (∃x)(Ax • Bx)
∼(∃x)(Cx • Bx)
(∀x)(Cx ⊃ Ax)

Accepted Answer

The answer of construct a model for each of the...

Question 11

select the best translation into predicate logic.
-Some settlements are not on the water.

Accepted Answer

A)  ∼(∃x)(Sx • ∼Wx) 
B)  ∼(∃x)(Sx • Wx) 
C)  (∃x)(Sx • ∼Wx) 
D)  (∃x)(Sx $ \lor $ ∼Wx)

Question 12

1. (∀x)(Ax ⊃ Bx)
2. (∃x)Ax
3. (∃x)Bx ⊃ (∃x)Dx
-Which of the following propositions is derivable from the given premises in M?

Accepted Answer

A)  (∃x)Dx 
B)  (∀x)Bx 
C)  (∃x)(Dx • Bx) 
D)  (∀x)(Dx • Bx) 
E)  (∀x)Ax

Question 13

1. (∀x)(Jx ⊃ Kx)
2. ∼(∀x)Kx
3. ∼(∀x)Ix $ \lor $ (∀x)Jx
-Which of the following propositions is an immediate (one-step) consequence in M of the given premises?

Accepted Answer

A)  ∼Kx 
B)  Ja ⊃ Kc 
C)  ∼(∀x)Ix $ \lor $ ∼(∃x)∼Jx 
D)  ∼(∃x)∼Ix $ \lor $ (∀x)Jx 
E)  Kx

Question 14

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)Ax
2. (∀x)∼Ax ⊃ ∼(∃x)Bx / Ba

Accepted Answer

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

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 • Rx) • (Sx • Tx)]

Accepted Answer

A)  Only if poodles fetch balls and sticks are they loved. 
B)  If poodles are loved, they will fetch balls and sticks. 
C)  Some loved poodles will fetch balls and sticks. 
D)  Some loved poodles will fetch balls and sticks, but some will not.

Question 16

Everything is material, or ideal or transcendental. All atoms are not ideal and not transcendental. And nothing is material. So there are no atoms.
-Which of the following propositions can also be proved from the premises of the above argument?

Accepted Answer

A)  (∃x)(Ax • Mx) 
B)  (∃x)Tx 
C)  (∀x)[∼Ax • (Ix • Tx)] 
D)  (∃x)Ix 
E)  (∀x)[∼Ax • (Ix $ \lor $ Tx)]

Question 17

derive the conclusions of each of the following arguments using the rules of inference for M, including conditional or indirect proof.
-1. (∀x)(Px ⊃ Qx)
2. ∼(∃x)[(Px • Rx) • Qx]
3. (∃x)Rx / ∼(∀x)Px

Accepted Answer

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

Question 18

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
-Not all the settlements have trading ports.

Accepted Answer

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

Question 19

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)] ⊃ (∀x)[(Px • Rx) ⊃ Tx)]

Accepted Answer

A)  If some poodles are neither abused nor loved, then all loved poodles will fetch sticks. 
B)  If some poodles are not abused but are loved, then all loved poodles will fetch sticks. 
C)  Some poodles are neither abused nor loved, and all loved poodles will fetch sticks. 
D)  Some poodles are abused and unloved, but all loved poodles will fetch sticks.

Question 20

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)(Mx • Ox) ⊃ (∃x)Nx
2. (∃x)(Px • Mx)
3. (∀x)(∼Px $ \lor $ Ox) / (∃x)Nx

Accepted Answer

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

Exam 4: Monadic Predicate Logic

derive the conclusions of each of the following arguments using the rules of inference for M, including conditional or indirect proof. -1. (∀x)Ix $\lor$ ∼(∃x)Hx 2. (∃x)Jx ⊃ ∼(∀x)Ix 3. Hc / (∀x)∼Jx

refer to the following formula: (∃x) [Mx • (∼Nc $\lor$ ∼Ox) ] ≡ (Py • Pb) -Which variables are bound by the '(∃x) '?

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 3. ∼(∀x)Ix $\lor$ (∀x)Jx / (∃x)∼Ix

refer to the following formula: (∃x)[(Ax • ∼Bx) • ∼(Cx $\lor$ Dx)] -List all of the subformulas in the scope of '(∃x)'.

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

Translate each of the following sentences into predicate logic, using the given constants and predicates. -Some visitors did not stay for dinner. (Sx: x stayed for dinner; Vx: x is a visitor)

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates. -Neither Gabriel nor Honoré play volleyball.

select the best translation into predicate logic. -Some settlements are not on the water.

1. (∀x) (Ax ⊃ Bx) 2. (∃x) Ax 3. (∃x) Bx ⊃ (∃x) Dx -Which of the following propositions is derivable from the given premises in M?

1. (∀x) (Jx ⊃ Kx) 2. ∼(∀x) Kx 3. ∼(∀x) Ix $\lor$ (∀x) Jx -Which of the following propositions is an immediate (one-step) consequence in M of the given premises?

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)Ax 2. (∀x)∼Ax ⊃ ∼(∃x)Bx / Ba

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 • Rx) • (Sx • Tx) ]

Everything is material, or ideal or transcendental. All atoms are not ideal and not transcendental. And nothing is material. So there are no atoms. -Which of the following propositions can also be proved from the premises of the above argument?

derive the conclusions of each of the following arguments using the rules of inference for M, including conditional or indirect proof. -1. (∀x)(Px ⊃ Qx) 2. ∼(∃x)[(Px • Rx) • Qx] 3. (∃x)Rx / ∼(∀x)Px

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 -Not all the settlements have trading ports.

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) ] ⊃ (∀x) [(Px • Rx) ⊃ Tx) ]

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)(Mx • Ox) ⊃ (∃x)Nx 2. (∃x)(Px • Mx) 3. (∀x)(∼Px $\lor$ Ox) / (∃x)Nx

Exam 4: Monadic Predicate Logic

derive the conclusions of each of the following arguments using the rules of inference for M, including conditional or indirect proof. -1. (∀x)Ix ∨ \lor ∨ ∼(∃x)Hx 2. (∃x)Jx ⊃ ∼(∀x)Ix 3. Hc / (∀x)∼Jx

refer to the following formula: (∃x) [Mx • (∼Nc ∨ \lor ∨ ∼Ox) ] ≡ (Py • Pb) -Which variables are bound by the '(∃x) '?

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 3. ∼(∀x)Ix ∨ \lor ∨ (∀x)Jx / (∃x)∼Ix

refer to the following formula: (∃x)[(Ax • ∼Bx) • ∼(Cx ∨ \lor ∨ Dx)] -List all of the subformulas in the scope of '(∃x)'.

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

Translate each of the following sentences into predicate logic, using the given constants and predicates. -Some visitors did not stay for dinner. (Sx: x stayed for dinner; Vx: x is a visitor)

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates. -Neither Gabriel nor Honoré play volleyball.

select the best translation into predicate logic. -Some settlements are not on the water.

1. (∀x) (Ax ⊃ Bx) 2. (∃x) Ax 3. (∃x) Bx ⊃ (∃x) Dx -Which of the following propositions is derivable from the given premises in M?

1. (∀x) (Jx ⊃ Kx) 2. ∼(∀x) Kx 3. ∼(∀x) Ix ∨ \lor ∨ (∀x) Jx -Which of the following propositions is an immediate (one-step) consequence in M of the given premises?

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)Ax 2. (∀x)∼Ax ⊃ ∼(∃x)Bx / Ba

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 • Rx) • (Sx • Tx) ]

Everything is material, or ideal or transcendental. All atoms are not ideal and not transcendental. And nothing is material. So there are no atoms. -Which of the following propositions can also be proved from the premises of the above argument?

derive the conclusions of each of the following arguments using the rules of inference for M, including conditional or indirect proof. -1. (∀x)(Px ⊃ Qx) 2. ∼(∃x)[(Px • Rx) • Qx] 3. (∃x)Rx / ∼(∀x)Px

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 -Not all the settlements have trading ports.

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) ] ⊃ (∀x) [(Px • Rx) ⊃ Tx) ]

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)(Mx • Ox) ⊃ (∃x)Nx 2. (∃x)(Px • Mx) 3. (∀x)(∼Px ∨ \lor ∨ Ox) / (∃x)Nx

derive the conclusions of each of the following arguments using the rules of inference for M, including conditional or indirect proof. -1. (∀x)Ix $\lor$ ∼(∃x)Hx 2. (∃x)Jx ⊃ ∼(∀x)Ix 3. Hc / (∀x)∼Jx

refer to the following formula: (∃x) [Mx • (∼Nc $\lor$ ∼Ox) ] ≡ (Py • Pb) -Which variables are bound by the '(∃x) '?

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 3. ∼(∀x)Ix $\lor$ (∀x)Jx / (∃x)∼Ix

refer to the following formula: (∃x)[(Ax • ∼Bx) • ∼(Cx $\lor$ Dx)] -List all of the subformulas in the scope of '(∃x)'.

1. (∀x) (Jx ⊃ Kx) 2. ∼(∀x) Kx 3. ∼(∀x) Ix $\lor$ (∀x) Jx -Which of the following propositions is an immediate (one-step) consequence in M of the given premises?

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)(Mx • Ox) ⊃ (∃x)Nx 2. (∃x)(Px • Mx) 3. (∀x)(∼Px $\lor$ Ox) / (∃x)Nx