Question 1

refer to the following formula: (∃x)[Mx • (∼Nc $ \lor $ ∼Ox)] ≡ (Py • Pb)
-Is the formula open or closed?

Accepted Answer

A)  Open 
B)  Closed 
A)  Open 
B)  Closed

Question 2

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates.
-Some yellow birds both chirp and sing.

Accepted Answer

A)  (∃x)[(Yx • Bx) • (Cx • Sx)] 
B)  (∃x)(Yx • Bx) • Sx 
C)  (∃x)(Sx • Bx) • Yx 
D)  (∃x)[(Yx • Bx) ⊃ (Cx • Sx)] 
E)  (∃x)[(Yx • Bx) ⊃ (Cx ⊃ Sx)] 
A)  (∃x)[(Yx • Bx) • (Cx • Sx)] 
B)  (∃x)(Yx • Bx) • Sx 
C)  (∃x)(Sx • Bx) • Yx 
D)  (∃x)[(Yx • Bx) ⊃ (Cx • Sx)] 
E)  (∃x)[(Yx • Bx) ⊃ (Cx ⊃ Sx)]

Question 3

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)(Cx • Dx) $ \lor $ (∃x)(Cx • ∼Dx)

Accepted Answer

A)  Logical truth 
B)  Not a logical truth. False valuation in a domain of 1 member, in which:
Ca: True Da: False 
C)  Not a logical truth. False valuation in a domain of 1 member, in which: Ca: False Da: False 
D)  Not a logical truth. False valuation in a domain of 2 members, in which: Ca: True Da: True
Cb: True Db: False 
E)  Not a logical truth. False valuation in a domain of 2 members, in which: Ca: True Da: False
Cb: True Db: True 
A)  Logical truth 
B)  Not a logical truth. False valuation in a domain of 1 member, in which:
Ca: True Da: False 
C)  Not a logical truth. False valuation in a domain of 1 member, in which: Ca: False Da: False 
D)  Not a logical truth. False valuation in a domain of 2 members, in which: Ca: True Da: True
Cb: True Db: False 
E)  Not a logical truth. False valuation in a domain of 2 members, in which: Ca: True Da: False
Cb: True Db: True

Question 4

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)Ix ⊃ (∀x)Kx
2. (∀x)[Jx • (Ix $ \lor $ Lx)]
3. (∀x)(Jx ⊃ ∼Lx) / (∀x)Kx

Accepted Answer

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

Question 5

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.
-Which of the following is the best translation into M of this argument?

Accepted Answer

A)  (∃x)(Jx • ∼Rx) ⊃ (∀x)[(Jx • Ix) ⊃ Wx] (∃x)[(Jx • Ix) • ∼Ax]
(∃x)(∼Ax • Wx) / (∀x)(Jx ⊃ Rx) 
B)  (∃x)(Jx • ∼Rx) ⊃ (∀x)[(Jx • Ix) ⊃ Wx] (∃x)[(Jx • Ix) • ∼Ax]
∼(∃x)(∼Ax • Wx) / (∀x)(Jx ⊃ Rx) 
C)  ∼(∃x)(Jx • Rx) ⊃ (∀x)[(Jx • Ix) ⊃ Wx] (∃x)[(Jx • Ix) • ∼Ax]
∼(∃x)(∼Ax • Wx) / (∀x)(Jx ⊃ Rx) 
D)  ∼(∃x)(Jx • ∼Rx) ⊃ (∀x)[(Jx • Ix) ⊃ Wx] (∃x)[(Jx • Ix) • ∼Ax]
∼(∃x)(Ax • Wx) / (∀x)(Jx ⊃ Rx) 
E)  (∃x)(Jx • ∼Rx) ⊃ (∀x)[(Jx • Ix) ⊃ Wx] (∃x)[(Jx • Ix) • Ax]
∼(∃x)∼(Ax • Wx) / (∀x)(Jx ⊃ Rx) 
A)  (∃x)(Jx • ∼Rx) ⊃ (∀x)[(Jx • Ix) ⊃ Wx] (∃x)[(Jx • Ix) • ∼Ax]
(∃x)(∼Ax • Wx) / (∀x)(Jx ⊃ Rx) 
B)  (∃x)(Jx • ∼Rx) ⊃ (∀x)[(Jx • Ix) ⊃ Wx] (∃x)[(Jx • Ix) • ∼Ax]
∼(∃x)(∼Ax • Wx) / (∀x)(Jx ⊃ Rx) 
C)  ∼(∃x)(Jx • Rx) ⊃ (∀x)[(Jx • Ix) ⊃ Wx] (∃x)[(Jx • Ix) • ∼Ax]
∼(∃x)(∼Ax • Wx) / (∀x)(Jx ⊃ Rx) 
D)  ∼(∃x)(Jx • ∼Rx) ⊃ (∀x)[(Jx • Ix) ⊃ Wx] (∃x)[(Jx • Ix) • ∼Ax]
∼(∃x)(Ax • Wx) / (∀x)(Jx ⊃ Rx) 
E)  (∃x)(Jx • ∼Rx) ⊃ (∀x)[(Jx • Ix) ⊃ Wx] (∃x)[(Jx • Ix) • Ax]
∼(∃x)∼(Ax • Wx) / (∀x)(Jx ⊃ Rx)

Question 6

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates.
-If Tranh takes a sabbatical then neither she nor Minh will feel overworked.

Accepted Answer

A)  St ⊃ (∼Ot $ \lor $ Om) 
B)  St ⊃ ∼(Ot $ \lor $ Om) 
C)  St ⊃ ∼(Ot $ \lor $ ∼Om) 
D)  St ⊃ (Ot $ \lor $ Om) 
E)  St ⊃ ∼(∼Ot $ \lor $ Om) 
A)  St ⊃ (∼Ot $ \lor $ Om) 
B)  St ⊃ ∼(Ot $ \lor $ Om) 
C)  St ⊃ ∼(Ot $ \lor $ ∼Om) 
D)  St ⊃ (Ot $ \lor $ Om) 
E)  St ⊃ ∼(∼Ot $ \lor $ Om)

Question 7

1. (∀x)Ix $ \lor $ ∼(∃x)Hx
2. (∃x)Jx ⊃ ∼(∀x)Ix
3. Hc / (∀x)∼Jx
-Which of the following propositions is not a likely last line of the indented sequence for an indirect proof of the given argument?

Accepted Answer

A)  Hc • ∼Hc 
B)  (∃x)Hx • ∼(∃x)Hx 
C)  Id • ∼Id 
D)  (∃x)Jx • ∼(∃x)Jx 
E)  (∀x)Ix • ∼(∀x)Ix 
A)  Hc • ∼Hc 
B)  (∃x)Hx • ∼(∃x)Hx 
C)  Id • ∼Id 
D)  (∃x)Jx • ∼(∃x)Jx 
E)  (∀x)Ix • ∼(∀x)Ix

Question 8

refer to the following formula:
∼(∀x){(Ix • Jx) ⊃ [Kx ≡ (La • Lb)]}
-Which variables are bound by the '(∀x)'?

Accepted Answer

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

Question 9

select the best translation into predicate logic.
-Tall athletes with determination either receive scholarships or play professional sports.

Accepted Answer

A)  (∃x){[(Tx • Ax) • Dx] ⊃ (Sx $ \lor $ Px)} 
B)  (∀x){(Sx $ \lor $ Px) ⊃ [(Tx • Ax) • Dx]} 
C)  (∀x){[(Tx • Ax) • Dx] ⊃ (Sx $ \lor $ Px)} 
D)  (∃x){[(Tx • Ax) • Dx] ≡ (Sx $ \lor $ Px)} 
A)  (∃x){[(Tx • Ax) • Dx] ⊃ (Sx $ \lor $ Px)} 
B)  (∀x){(Sx $ \lor $ Px) ⊃ [(Tx • Ax) • Dx]} 
C)  (∀x){[(Tx • Ax) • Dx] ⊃ (Sx $ \lor $ Px)} 
D)  (∃x){[(Tx • Ax) • Dx] ≡ (Sx $ \lor $ Px)}

Question 10

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
-Everyone is a theist unless someone is a skeptic and not an apriorist.

Accepted Answer

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

Question 11

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

Accepted Answer

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

Question 12

select the best translation into predicate logic.
-Some apriorist is a skeptic if, and only if, s/he is an inconsistent empiricist.

Accepted Answer

A)  (∃x)[(Ax • Sx) ⊃ (Ex • ∼Cx)] 
B)  (∃x)[(Ax • Sx) ≡ (Ex $ \lor $ ∼Cx)] 
C)  (∃x)[(Ax • Sx) ≡ (Ex • ∼Cx)] 
D)  (∃x)[(Ax • Sx) ⊃ (Ex $ \lor $ ∼Cx)] 
A)  (∃x)[(Ax • Sx) ⊃ (Ex • ∼Cx)] 
B)  (∃x)[(Ax • Sx) ≡ (Ex $ \lor $ ∼Cx)] 
C)  (∃x)[(Ax • Sx) ≡ (Ex • ∼Cx)] 
D)  (∃x)[(Ax • Sx) ⊃ (Ex $ \lor $ ∼Cx)]

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
-Some rationalists who are skeptics are not theists.

Accepted Answer

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

Question 14

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) ⊃ ∼Rx]

Accepted Answer

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

Question 15

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 anything is stuck in traffic, Bruno will be mad if it is late. Everything is neither annoyed nor not late. If Bruno is mad, then everything is annoyed. So something is not stuck in traffic. (b: Bruno; Ax: x is annoyed; Lx: x is late; Mx: x is mad; Sx: x is stuck in traffic)

Accepted Answer

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

Question 16

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)
2. (∃x)(Ax • Cx) / ∼(∀x)(Bx ⊃ ∼Cx)

Accepted Answer

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

Question 17

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

Accepted Answer

A)  (∀x)Jx 
B)  (∃x)∼Ix 
C)  (∀x)Kx 
D)  (∃x)Ix 
E)  (∀x)(Kx ⊃ Jx) 
A)  (∀x)Jx 
B)  (∃x)∼Ix 
C)  (∀x)Kx 
D)  (∃x)Ix 
E)  (∀x)(Kx ⊃ Jx)

Question 18

consider the following domain, assignment of objects in the domain, and assignments sets to predicates.
Domain = {1, 2, 3, ..., 28, 29, 30}
N = {1, 2, 3, ..., 28, 29, 30}
E = {2, 4, 6, ..., 28, 30}
O = {1, 3, 5, ..., 27, 29}
P = (2, 3, 5, 7, 11, 13, 17, 19, 23, 29}
a = 1
b = 2
c = 28
-Given the customary truth tables, which of the following theories is modeled by the above interpretation?

Accepted Answer

A)  (∃x)(Px • Ex)
(∃x)(Ex • Ox) 
B)  (∃x)(Px • Ex)
(∃x)[(Ex • Ox) • ∼Px] 
C)  (∃x)(Px • Ex)
(∀x)(Px ⊃ Ox) 
D)  (∃x)(Px • Ex)
(∃x)(Px • Ox) 
E)  (∃x)(Px • Ex)
(∀x)(Ox ⊃ Px) 
A)  (∃x)(Px • Ex)
(∃x)(Ex • Ox) 
B)  (∃x)(Px • Ex)
(∃x)[(Ex • Ox) • ∼Px] 
C)  (∃x)(Px • Ex)
(∀x)(Px ⊃ Ox) 
D)  (∃x)(Px • Ex)
(∃x)(Px • Ox) 
E)  (∃x)(Px • Ex)
(∀x)(Ox ⊃ Px)

Question 19

select a counterexample for the given invalid argument.
-1. (∃x)(Gx • Hx)
2) (∃x)(Gx • Jx)
3) (∀x)(Jx ⊃ Kx) / (∃x)(Hx • Jx)

Accepted Answer

A)  Counterexample in a domain of 2 members, in which: Ga: True Ha: True Ja: True Ka: True
Gb: True Hb: True Jb: True Kb: False 
B)  Counterexample in a domain of 2 members, in which: Ga: True Ha: True Ja: True Ka: True
Gb: False Hb: True Jb: True Kb: False 
C)  Counterexample in a domain of 2 members, in which: Ga: True Ha: True Ja: True Ka: False
Gb: True Hb: True Jb: True Kb: False 
D)  Counterexample in a domain of 2 members, in which: Ga: False Ha: True Ja: True Ka: True
Gb: False Hb: True Jb: True Kb: True 
E)  Counterexample in a domain of 2 members, in which: Ga: True Ha: False Ja: True Ka: True
Gb: True Hb: True Jb: False Kb: False 
A)  Counterexample in a domain of 2 members, in which: Ga: True Ha: True Ja: True Ka: True
Gb: True Hb: True Jb: True Kb: False 
B)  Counterexample in a domain of 2 members, in which: Ga: True Ha: True Ja: True Ka: True
Gb: False Hb: True Jb: True Kb: False 
C)  Counterexample in a domain of 2 members, in which: Ga: True Ha: True Ja: True Ka: False
Gb: True Hb: True Jb: True Kb: False 
D)  Counterexample in a domain of 2 members, in which: Ga: False Ha: True Ja: True Ka: True
Gb: False Hb: True Jb: True Kb: True 
E)  Counterexample in a domain of 2 members, in which: Ga: True Ha: False Ja: True Ka: True
Gb: True Hb: True Jb: False Kb: False

Question 20

refer to the following formula: (∀x)[(Ex $ \lor $ Fx) ⊃ (Gx • Hd)]
-Which variables are bound by the '(∀x)'?

Accepted Answer

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

refer to the following formula: (∃x)[Mx • (∼Nc $\lor$ ∼Ox)] ≡ (Py • Pb) -Is the formula open or closed?

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates. -Some yellow birds both chirp and sing.

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)(Cx • Dx) $\lor$ (∃x)(Cx • ∼Dx)

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)Ix ⊃ (∀x)Kx 2. (∀x)[Jx • (Ix $\lor$ Lx)] 3. (∀x)(Jx ⊃ ∼Lx) / (∀x)Kx

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates. -If Tranh takes a sabbatical then neither she nor Minh will feel overworked.

1. (∀x)Ix $\lor$ ∼(∃x)Hx 2. (∃x)Jx ⊃ ∼(∀x)Ix 3. Hc / (∀x)∼Jx -Which of the following propositions is not a likely last line of the indented sequence for an indirect proof of the given argument?

refer to the following formula: ∼(∀x){(Ix • Jx) ⊃ [Kx ≡ (La • Lb)]} -Which variables are bound by the '(∀x)'?

select the best translation into predicate logic. -Tall athletes with determination either receive scholarships or play professional sports.

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 -Everyone is a theist unless someone is a skeptic and not an apriorist.

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

select the best translation into predicate logic. -Some apriorist is a skeptic if, and only if, s/he is an inconsistent empiricist.

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 -Some rationalists who are skeptics are not theists.

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) ⊃ ∼Rx]

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) 2. (∃x)(Ax • Cx) / ∼(∀x)(Bx ⊃ ∼Cx)

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

select a counterexample for the given invalid argument. -1. (∃x)(Gx • Hx) 2) (∃x)(Gx • Jx) 3) (∀x)(Jx ⊃ Kx) / (∃x)(Hx • Jx)

refer to the following formula: (∀x)[(Ex $\lor$ Fx) ⊃ (Gx • Hd)] -Which variables are bound by the '(∀x)'?

Introducing Logic

Propositional Logic: Syntax and Semantic

Inference in Propositional Logic

Full First-Order Logic

Filters

Exam 4: Monadic Predicate Logic

refer to the following formula: (∃x)[Mx • (∼Nc ∨ \lor ∨ ∼Ox)] ≡ (Py • Pb) -Is the formula open or closed?