Question 1

refer to the following formula: (∃x)[(Ax • ∼Bx) • ∼(Cx $ \lor $ Dx)]
-Is the formula open or closed?

Accepted Answer

A)  Open 
B)  Closed

Question 2

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 and settlements are nicely placed and productive.

Accepted Answer

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

Question 3

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

Accepted Answer

A)  (∀x)[Lx ⊃ (Kx ⊃ Jx)] 
B)  (∀x)[Kx ⊃ (Jx • Lx)] 
C)  (∀x)[Jx ⊃ (Kx • Lx)] 
D)  Kx • ∼Lx 
E)  (∀x)[Jx ⊃ (Kx • ∼Lx)]

Question 4

Some websites have open comments which are not anonymous. Any website is either anonymous or requires a login. So something with open comments requires a login.
-Which of the following claims can also be derived from the premises of this argument?

Accepted Answer

A)  Ab $ \lor $ Lb 
B)  (∀x)(Ax $ \lor $ Lx) 
C)  (∀x)(Ox • Lx) 
D)  (∃x)Ax 
E)  (∃x)∼Wx

Question 5

consider the following domain, assignment of objects in the domain, and assignments sets to predicates.
Domain = {Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, Pluto} 
P = {Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune}
I = {Mercury, Venus}
O = {Mars, Jupiter, Saturn, Uranus, Neptune}
a = Mercury b = Jupiter c = Saturn
d = Pluto
-Given the customary truth tables, which of the following theories is modeled by the above interpretation?

Accepted Answer

A)  Pa • ∼Pb
Ia • ∼Id 
B)  Pa • ∼Pd
∼Ia • ∼Id 
C)  Pa • ∼Pd
Oa • ∼Id 
D)  Pa • ∼Pd
Ob • Od 
E)  Pa • ∼Pd
Ia • ∼Id

Question 6

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

Accepted Answer

A)  Js ⊃ ~Ls 
B)  Kx $ \lor $ Lx 
C)  Js ⊃ ~Lx 
D)  Kx $ \lor $ Ly 
E)  Kn $ \lor $ Lm

Question 7

provide a conterexample in a finite domain to each given invalid argument.
-1. (∀x)(Kx ⊃ ∼Lx)
2. (∃x)(Mx • Lx) / (∀x)(Kx ⊃ ∼Mx)

Accepted Answer

The answer of provide a conterexample in a finite domain...

Question 8

1. (∀x)[(Px $ \lor $ Qx) ⊃ (Rx • ∼Sx)]
2. (∀x)[Rx ⊃ (Tx ⊃ ∼Sx)]
-Consider assuming 'Px' for conditional proof. Which of the following propositions is an immediate (one-step) consequence in M of the given premises with that further assumption for conditional proof?

Accepted Answer

A)  Ra ⊃ (Tb ⊃ ∼Sc) 
B)  (∀x)Px 
C)  Px $ \lor $ Qx 
D)  Tx ⊃ ∼Sx 
E)  Rx • ∼Sx

Question 9

Translate each of the following sentences into predicate logic, using the given constants and predicates.
-Izzy takes linear algebra only if she does not take discrete mathematics. (i: Izzy; Dx: x takes discrete mathematics; Lx: x takes linear algebra)

Accepted Answer

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

Question 10

determine whether the given argument is valid or invalid. If it is invalid, select a counterexample.
-1. (∃x)[(Ax • Bx) • Cx]
2) (∀x)[(Ax • ∼Cx) ⊃ ∼Bx] / (∃x)(Ax • ∼Bx)

Accepted Answer

A)  Valid 
B)  Invalid. Counterexample in a domain of 1 member, in which:
Aa: True Ba: True Ca: False 
C)  Invalid. Counterexample in a domain of 1 member, in which:
Aa: True Ba: False Ca: True 
D)  Invalid. Counterexample in a domain of 1 member, in which:
Aa: True Ba: True Ca: True 
E)  Invalid. Counterexample in a domain of 1 member, in which:
Aa: False Ba: True Ca: True

Question 11

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 ⊃ Bx)
2. (∃x)Ax
3. (∃x)Bx ⊃ (∃x)Dx / (∃x)Dx

Accepted Answer

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

Question 12

determine whether the given formula is a logical truth of M or not. If it is a logical truth, provide a proof of the formula. If it is not a logical truth, provide a counterexample in a finite domain.
-(∃x)(Ix • Jx) ⊃ [(∀x)Ix ⊃ (∀x)Jx]

Accepted Answer

The answer of determine whether the given formula is a...

Question 13

1. ∼(∃x)[Fx • (Gx • Hx)]
2. ∼(∃x)(Ix • ∼Fx)
-Which of the following propositions is an immediate (one-step) consequence in M of the given premises?

Accepted Answer

A)  (∀x)∼[Fx • (Gx • Hx)] 
B)  Fx • (Gx • Hx) 
C)  Fa • (Ga • Ha) 
D)  (∃x)∼[Fx • (Gx • Hx)] 
E)  ∼(∀x)[Fx • (Gx • Hx)]

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)(Kx $ \lor $ Lx)
2. (∀x)(Jx ⊃ ~Lx) / (∃x)(~Jx $ \lor $ Kx)

Accepted Answer

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

Question 15

provide a conterexample in a finite domain to each given invalid argument.
-1. (∃x)(Hx • Ix)
2. (∃x)(Hx • ∼Ix)
3. (∀x)(Jx ⊃ Ix) / (∀x)(Jx ⊃ Hx)

Accepted Answer

The answer of provide a conterexample in a finite domain...

Question 16

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
-All tall athletes work hard.

Accepted Answer

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

Question 17

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 is a good assumption for indirect proof for the above argument?

Accepted Answer

A)  ∼(∃x)Ax 
B)  (∃x)Ax 
C)  ∼(∀x)Ax 
D)  (∀x)Ax 
E)  (∀x)∼Ax

Question 18

Translate each of the following sentences into predicate logic, using the given constants and predicates.
-All mammals feed their young. (Fx: x feeds their young; Mx: x is a mammal)

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.
-If Carla works for an airline, then Darlene doesn't. (c: Carla; d: Darlene; Ax: x works for an
airline)

Accepted Answer

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

Question 20

select the best translation into predicate logic.
-Only tall athletes play professional basketball.

Accepted Answer

A)  (∀x)[Px ⊃ (Tx • Ax)] 
B)  (∀x)[(Tx • Ax) ⊃ Px] 
C)  (∀x)[(Tx $ \lor $ Ax) ⊃ Px] 
D)  (∀x)[Px ≡ (Tx • Ax)]

Exam 4: Monadic Predicate Logic

refer to the following formula: (∃x) [(Ax • ∼Bx) • ∼(Cx $\lor$ Dx) ] -Is the formula open or closed?

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 and settlements are nicely placed and productive.

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

Some websites have open comments which are not anonymous. Any website is either anonymous or requires a login. So something with open comments requires a login. -Which of the following claims can also be derived from the premises of this argument?

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

provide a conterexample in a finite domain to each given invalid argument. -1. (∀x)(Kx ⊃ ∼Lx) 2. (∃x)(Mx • Lx) / (∀x)(Kx ⊃ ∼Mx)

1. (∀x) [(Px $\lor$ Qx) ⊃ (Rx • ∼Sx) ] 2. (∀x) [Rx ⊃ (Tx ⊃ ∼Sx) ] -Consider assuming 'Px' for conditional proof. Which of the following propositions is an immediate (one-step) consequence in M of the given premises with that further assumption for conditional proof?

Translate each of the following sentences into predicate logic, using the given constants and predicates. -Izzy takes linear algebra only if she does not take discrete mathematics. (i: Izzy; Dx: x takes discrete mathematics; Lx: x takes linear algebra)

determine whether the given argument is valid or invalid. If it is invalid, select a counterexample. -1. (∃x) [(Ax • Bx) • Cx] 2) (∀x) [(Ax • ∼Cx) ⊃ ∼Bx] / (∃x) (Ax • ∼Bx)

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 ⊃ Bx) 2. (∃x)Ax 3. (∃x)Bx ⊃ (∃x)Dx / (∃x)Dx

determine whether the given formula is a logical truth of M or not. If it is a logical truth, provide a proof of the formula. If it is not a logical truth, provide a counterexample in a finite domain. -(∃x)(Ix • Jx) ⊃ [(∀x)Ix ⊃ (∀x)Jx]

1. ∼(∃x) [Fx • (Gx • Hx) ] 2. ∼(∃x) (Ix • ∼Fx) -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)(Kx $\lor$ Lx) 2. (∀x)(Jx ⊃ ~Lx) / (∃x)(~Jx $\lor$ Kx)

provide a conterexample in a finite domain to each given invalid argument. -1. (∃x)(Hx • Ix) 2. (∃x)(Hx • ∼Ix) 3. (∀x)(Jx ⊃ Ix) / (∀x)(Jx ⊃ Hx)

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 -All tall athletes work hard.

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 is a good assumption for indirect proof for the above argument?

Translate each of the following sentences into predicate logic, using the given constants and predicates. -All mammals feed their young. (Fx: x feeds their young; Mx: x is a mammal)

Translate each of the following sentences into predicate logic, using the given constants and predicates. -If Carla works for an airline, then Darlene doesn't. (c: Carla; d: Darlene; Ax: x works for an airline)

select the best translation into predicate logic. -Only tall athletes play professional basketball.

Exam 4: Monadic Predicate Logic

refer to the following formula: (∃x) [(Ax • ∼Bx) • ∼(Cx ∨ \lor ∨ Dx) ] -Is the formula open or closed?

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 and settlements are nicely placed and productive.

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

Some websites have open comments which are not anonymous. Any website is either anonymous or requires a login. So something with open comments requires a login. -Which of the following claims can also be derived from the premises of this argument?

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

provide a conterexample in a finite domain to each given invalid argument. -1. (∀x)(Kx ⊃ ∼Lx) 2. (∃x)(Mx • Lx) / (∀x)(Kx ⊃ ∼Mx)

1. (∀x) [(Px ∨ \lor ∨ Qx) ⊃ (Rx • ∼Sx) ] 2. (∀x) [Rx ⊃ (Tx ⊃ ∼Sx) ] -Consider assuming 'Px' for conditional proof. Which of the following propositions is an immediate (one-step) consequence in M of the given premises with that further assumption for conditional proof?

Translate each of the following sentences into predicate logic, using the given constants and predicates. -Izzy takes linear algebra only if she does not take discrete mathematics. (i: Izzy; Dx: x takes discrete mathematics; Lx: x takes linear algebra)

determine whether the given argument is valid or invalid. If it is invalid, select a counterexample. -1. (∃x) [(Ax • Bx) • Cx] 2) (∀x) [(Ax • ∼Cx) ⊃ ∼Bx] / (∃x) (Ax • ∼Bx)

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 ⊃ Bx) 2. (∃x)Ax 3. (∃x)Bx ⊃ (∃x)Dx / (∃x)Dx

determine whether the given formula is a logical truth of M or not. If it is a logical truth, provide a proof of the formula. If it is not a logical truth, provide a counterexample in a finite domain. -(∃x)(Ix • Jx) ⊃ [(∀x)Ix ⊃ (∀x)Jx]

1. ∼(∃x) [Fx • (Gx • Hx) ] 2. ∼(∃x) (Ix • ∼Fx) -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)(Kx ∨ \lor ∨ Lx) 2. (∀x)(Jx ⊃ ~Lx) / (∃x)(~Jx ∨ \lor ∨ Kx)

provide a conterexample in a finite domain to each given invalid argument. -1. (∃x)(Hx • Ix) 2. (∃x)(Hx • ∼Ix) 3. (∀x)(Jx ⊃ Ix) / (∀x)(Jx ⊃ Hx)

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 -All tall athletes work hard.

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 is a good assumption for indirect proof for the above argument?

Translate each of the following sentences into predicate logic, using the given constants and predicates. -All mammals feed their young. (Fx: x feeds their young; Mx: x is a mammal)

Translate each of the following sentences into predicate logic, using the given constants and predicates. -If Carla works for an airline, then Darlene doesn't. (c: Carla; d: Darlene; Ax: x works for an airline)

select the best translation into predicate logic. -Only tall athletes play professional basketball.

refer to the following formula: (∃x) [(Ax • ∼Bx) • ∼(Cx $\lor$ Dx) ] -Is the formula open or closed?

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

1. (∀x) [(Px $\lor$ Qx) ⊃ (Rx • ∼Sx) ] 2. (∀x) [Rx ⊃ (Tx ⊃ ∼Sx) ] -Consider assuming 'Px' for conditional proof. Which of the following propositions is an immediate (one-step) consequence in M of the given premises with that further assumption for conditional proof?

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)(Kx $\lor$ Lx) 2. (∀x)(Jx ⊃ ~Lx) / (∃x)(~Jx $\lor$ Kx)