Question 1

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)(Jx • ∼Kx) ⊃ (∃x)(Lx • Mx)
2. (∃x)(Jx • Lx)
3. ∼(∃x)(Jx • Kx) / ∼(∀x)(Lx ⊃ ∼Mx)

Accepted Answer

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

Question 2

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

Accepted Answer

A)  Valid 
B)  Invalid. Counterexample in a domain of 1 member, in which:
Da: True Ea: True Fa: True Ga: True 
C)  Invalid. Counterexample in a domain of 1 member, in which:
Da: True Ea: True Fa: True Ga: False 
D)  Invalid. Counterexample in a domain of 1 member, in which:
Da: True Ea: True Fa: False Ga: True 
E)  Invalid. Counterexample in a domain of 1 member, in which:
Da: False Ea: True Fa: True Ga: True

Question 3

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
-Berkeley is an empiricist and Hume is not an apriorist.

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

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
-All idealists are apriorists, but not theists.

Accepted Answer

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

Question 6

select a counterexample for the given invalid argument.
-1. (∃x)(∼Ax ≡ Cx)
2) (∃x)(Ax • Cx)
3) (∀x)(Bx ⊃ Ax) / (∀x)(Cx ⊃ Bx)

Accepted Answer

A)  Counterexample in a domain of 2 members, in which: Aa: True Ba: False Ca: True
Ab: True Bb: True Cb: False 
B)  Counterexample in a domain of 2 members, in which: Aa: False Ba: False Ca: True
Ab: True Bb: True Cb: False 
C)  Counterexample in a domain of 2 members, in which: Aa: True Ba: True Ca: True
Ab: True Bb: True Cb: False 
D)  Counterexample in a domain of 2 members, in which: Aa: True Ba: False Ca: True
Ab: False Bb: True Cb: False 
E)  Counterexample in a domain of 2 members, in which: Aa: True Ba: False Ca: True
Ab: True Bb: False Cb: True

Question 7

provide a conterexample in a finite domain to each given invalid argument.
-1. (∃x)Sx
2. (∀x)[Sx ⊃ (Tx ⊃ ∼Ux)]
3. Ua • Ub
4. (∃x)∼Ux / (∃x)(Sx • ∼Tx)

Accepted Answer

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

Question 8

Translate each of the following sentences into predicate logic, using the given constants and predicates.
-Some cherries are red. (Cx: x is a cherry; Rx: x is red)

Accepted Answer

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

Question 9

refer to the following formula: (∃x)[Mx • (∼Nc $ \lor $ ∼Ox)] ≡ (Py • Pb)
-What is the main operator of the given formula?

Accepted Answer

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

Question 10

refer to the following formula: (∀x)[(Ex $ \lor $ Fx) ⊃ (Gx • Hd)]
-Which wffs below are not in the scope of '(∀x)'?

Accepted Answer

A)  Ex 
B)  Hd 
C)  Ex $ \lor $ Fx 
D)  All of the above. 
E)  None of the above.

Question 11

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)[Ax • (Bx $ \lor $ Cx)]
2. (∀x)(Bx ⊃ ∼Cx)
3. (∃x)Bx
4. Ca / (∃x)(Ax • Cx)

Accepted Answer

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

Question 12

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates.
-Izzy takes linear algebra only if she does not take discrete mathematics.

Accepted Answer

A)  ∼Li ⊃ Di 
B)  Di ≡ ∼Li 
C)  Li ⊃ ∼Di 
D)  Li ≡ Di 
E)  ∼Di ⊃ ∼Li

Question 13

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates.
-Bonita doesn't study law; she's pre-med.

Accepted Answer

A)  ∼Lb • Mb 
B)  ∼Lb ⊃ Mb 
C)  ∼Bl $ \lor $ Bm 
D)  ∼Bl ⊃ Bm 
E)  Lb • Mb

Question 14

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates.
-Farzona's dropping art history is a sufficient condition for her being unhappy.

Accepted Answer

A)  Uf ≡ Af 
B)  Af ⊃ Uf 
C)  Fa ≡ Uf 
D)  Af • Fu 
E)  Fa ≡ Fu

Question 15

refer to the following formula:
∼(∀x){(Ix • Jx) ⊃ [Kx ≡ (La • Lb)]}
-Is the formula open or closed?

Accepted Answer

A)  Open 
B)  Closed

Question 16

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 claims can also be derived from the premises of this argument?

Accepted Answer

A)  (∃x)Lx 
B)  ∼Sb $ \lor $ ∼Lb 
C)  ∼Mb 
D)  All of the above. 
E)  None of the above.

Question 17

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates.
-Some visitors did not stay for dinner.

Accepted Answer

A)  (∀x)(∼Vx • Sx) 
B)  (∃x)(∼Vx • ∼Sx) 
C)  (∃x)(Vx ⊃ ∼Sx) 
D)  (∃x)(Vx • ∼Sx) 
E)  (∀x)(Vx • ∼Sx)

Question 18

use the given interpretations to translate each sentence of predicate logic into natural, English sentences.
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

The answer of use the given interpretations to translate each...

Question 19

Translate each of the following sentences into predicate logic, using the given constants and predicates.
-No humans don't have a mother. (Hx: x is a human; Mx: x has a mother)

Accepted Answer

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

Question 20

refer to the following formula: (∃x)[(Ax • ∼Bx) • ∼(Cx $ \lor $ Dx)]
-Which of the following variables in the formula are free?

Accepted Answer

A)  The x that follows the A. 
B)  The x that follows the B. 
C)  The x that follows the C. 
D)  All of the above. 
E)  None of the above.

Exam 4: Monadic Predicate Logic

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)(Jx • ∼Kx) ⊃ (∃x)(Lx • Mx) 2. (∃x)(Jx • Lx) 3. ∼(∃x)(Jx • Kx) / ∼(∀x)(Lx ⊃ ∼Mx)

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

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 -Berkeley is an empiricist and Hume is not an apriorist.

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

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 -All idealists are apriorists, but not theists.

select a counterexample for the given invalid argument. -1. (∃x) (∼Ax ≡ Cx) 2) (∃x) (Ax • Cx) 3) (∀x) (Bx ⊃ Ax) / (∀x) (Cx ⊃ Bx)

provide a conterexample in a finite domain to each given invalid argument. -1. (∃x)Sx 2. (∀x)[Sx ⊃ (Tx ⊃ ∼Ux)] 3. Ua • Ub 4. (∃x)∼Ux / (∃x)(Sx • ∼Tx)

Translate each of the following sentences into predicate logic, using the given constants and predicates. -Some cherries are red. (Cx: x is a cherry; Rx: x is red)

refer to the following formula: (∃x)[Mx • (∼Nc $\lor$ ∼Ox)] ≡ (Py • Pb) -What is the main operator of the given formula?

refer to the following formula: (∀x) [(Ex $\lor$ Fx) ⊃ (Gx • Hd) ] -Which wffs below are not in the scope of '(∀x) '?

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)[Ax • (Bx $\lor$ Cx)] 2. (∀x)(Bx ⊃ ∼Cx) 3. (∃x)Bx 4. Ca / (∃x)(Ax • Cx)

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates. -Izzy takes linear algebra only if she does not take discrete mathematics.

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates. -Bonita doesn't study law; she's pre-med.

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates. -Farzona's dropping art history is a sufficient condition for her being unhappy.

refer to the following formula: ∼(∀x) {(Ix • Jx) ⊃ [Kx ≡ (La • Lb) ]} -Is the formula open or closed?

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 claims can also be derived from the premises of this argument?

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates. -Some visitors did not stay for dinner.

use the given interpretations to translate each sentence of predicate logic into natural, English sentences. 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. -No humans don't have a mother. (Hx: x is a human; Mx: x has a mother)

refer to the following formula: (∃x) [(Ax • ∼Bx) • ∼(Cx $\lor$ Dx) ] -Which of the following variables in the formula are free?