Question 1

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates.
-No humans don't have a mother.

Accepted Answer

A)  (∀x)(Hx ⊃ ∼∼Mx) 
B)  (∃x)(Hx ⊃ ∼Mx) 
C)  ∼(∀x)(Hx ⊃ Mx) 
D)  (∀x)(Hx ⊃ ∼Mx) 
E)  (∃x)(Hx • ∼Mx) 
A)  (∀x)(Hx ⊃ ∼∼Mx) 
B)  (∃x)(Hx ⊃ ∼Mx) 
C)  ∼(∀x)(Hx ⊃ Mx) 
D)  (∀x)(Hx ⊃ ∼Mx) 
E)  (∃x)(Hx • ∼Mx)

Question 2

Things are pleasant if, and only if, they are not too crowded. Everything too crowded is noisy. So if something isn't noisy, then something is pleasant.
-Which of the following is the best translation into M of this argument?

Accepted Answer

A)  (∀x)(Px ⊃ ∼Cx) (∀x)(Cx ⊃ Nx) / (∃x)(∼Nx • Px) 
B)  (∀x)(Px ≡ ∼Cx) (∀x)(Cx ⊃ Nx) / ∼(∃x)Nx ⊃ (∃x)Px 
C)  (∀x)(Px ⊃ ∼Cx) (∀x)(Cx ⊃ Nx) / (∃x)∼Nx ⊃ (∃x)Px 
D)  (∀x)(Px ≡ ∼Cx) (∀x)(Cx ⊃ Nx) / (∃x)∼Nx ⊃ (∃x)Px 
E)  (∀x)(Px ≡ ∼Cx) (∀x)(Cx ⊃ Nx) / (∃x)(∼Nx • Px) 
A)  (∀x)(Px ⊃ ∼Cx) (∀x)(Cx ⊃ Nx) / (∃x)(∼Nx • Px) 
B)  (∀x)(Px ≡ ∼Cx) (∀x)(Cx ⊃ Nx) / ∼(∃x)Nx ⊃ (∃x)Px 
C)  (∀x)(Px ⊃ ∼Cx) (∀x)(Cx ⊃ Nx) / (∃x)∼Nx ⊃ (∃x)Px 
D)  (∀x)(Px ≡ ∼Cx) (∀x)(Cx ⊃ Nx) / (∃x)∼Nx ⊃ (∃x)Px 
E)  (∀x)(Px ≡ ∼Cx) (∀x)(Cx ⊃ Nx) / (∃x)(∼Nx • Px)

Question 3

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

Accepted Answer

The answer of refer to the following formula: (∀x)[(Ex \(...

Question 4

Translate each of the following sentences into predicate logic, using the given constants and predicates.
-Kyrone has a thriving practice if Jalissa stops touring. (j: Jalissa; k: Kyrone; Px: x has a thriving practice; Tx: x stops touring)

Accepted Answer

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

Question 5

select the best translation into predicate logic.
-Not all the settlements have trading ports.

Accepted Answer

A)  (∀x)(Sx ⊃ ∼Tx) 
B)  ∼(∀x)(Sx ⊃ Tx) 
C)  ∼(∀x)(Sx ⊃ ∼Tx) 
D)  (∀x)(Sx ⊃ Tx) 
A)  (∀x)(Sx ⊃ ∼Tx) 
B)  ∼(∀x)(Sx ⊃ Tx) 
C)  ∼(∀x)(Sx ⊃ ∼Tx) 
D)  (∀x)(Sx ⊃ Tx)

Question 6

select the best translation into predicate logic.
-Some tall athletes don't receive scholarships.

Accepted Answer

A)  (∀x)[(Ax • Tx) ⊃ ∼Sx] 
B)  (∃x)[(Ax • Tx) • ∼Sx] 
C)  (∃x)[(Ax $ \lor $ Tx) • ∼Sx] 
D)  (∃x)[(Ax • Tx) ⊃ ∼Sx] 
A)  (∀x)[(Ax • Tx) ⊃ ∼Sx] 
B)  (∃x)[(Ax • Tx) • ∼Sx] 
C)  (∃x)[(Ax $ \lor $ Tx) • ∼Sx] 
D)  (∃x)[(Ax • Tx) ⊃ ∼Sx]

Question 7

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

Accepted Answer

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

Question 8

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
-If Tortuga is a city, then some settlements are not nicely placed.

Accepted Answer

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

Question 9

refer to the following formula: (∃x)[Mx • (∼Nc $ \lor $ ∼Ox)] ≡ (Py • Pb)
-Which wffs below are not in the scope of '(∃x)'?

Accepted Answer

A)  ∼(Py • Pb) 
B)  Mx 
C)  Nc 
D)  Mx • (∼Nc $ \lor $ ∼Ox) 
E)  None of the above. 
A)  ∼(Py • Pb) 
B)  Mx 
C)  Nc 
D)  Mx • (∼Nc $ \lor $ ∼Ox) 
E)  None of the above.

Question 10

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates.
-No red flowers are in the garden.

Accepted Answer

A)  ∼(∀x)[(Rx • Fx) ⊃ Gx] 
B)  (∀x)[(Rx • Fx) ⊃ ∼Gx] 
C)  (∀x)∼[(Rx • Fx) ⊃ Gx] 
D)  (∃x)[(Rx • Fx) ⊃ ∼Gx] 
E)  (∃x)[(Rx • Fx) • ∼Gx] 
A)  ∼(∀x)[(Rx • Fx) ⊃ Gx] 
B)  (∀x)[(Rx • Fx) ⊃ ∼Gx] 
C)  (∀x)∼[(Rx • Fx) ⊃ Gx] 
D)  (∃x)[(Rx • Fx) ⊃ ∼Gx] 
E)  (∃x)[(Rx • Fx) • ∼Gx]

Question 11

select the best translation into predicate logic.
-Everyone is a theist unless someone is a skeptic and not an apriorist.

Accepted Answer

A)  (∀x)(Px ⊃ Tx) ⊃ (∃x)(Sx • ∼Ax) 
B)  (∀x)(Px ⊃ Tx) $ \lor $ (∃x)(Sx $ \lor $ ∼Ax) 
C)  (∀x)(Px ⊃ Tx) ⊃ (∃x)(Sx $ \lor $ ∼Ax) 
D)  (∀x)(Px ⊃ Tx) $ \lor $ (∃x)(Sx • ∼Ax) 
A)  (∀x)(Px ⊃ Tx) ⊃ (∃x)(Sx • ∼Ax) 
B)  (∀x)(Px ⊃ Tx) $ \lor $ (∃x)(Sx $ \lor $ ∼Ax) 
C)  (∀x)(Px ⊃ Tx) ⊃ (∃x)(Sx $ \lor $ ∼Ax) 
D)  (∀x)(Px ⊃ Tx) $ \lor $ (∃x)(Sx • ∼Ax)

Question 12

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 • Rx) • (Sx • Tx)]

Accepted Answer

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

Question 13

refer to the following formula: (∀x)[(Ex $ \lor $ Fx) ⊃ (Gx • Hd)]
-Are there any free variables? If so, which are they?

Accepted Answer

The answer of refer to the following formula: (∀x)[(Ex \(...

Question 14

refer to the following formula:
∼(∀x){(Ix • Jx) ⊃ [Kx ≡ (La • Lb)]}
-Which wffs below are not in the scope of '(∀x)'?

Accepted Answer

A)  Lb 
B)  La 
C)  La • Lb 
D)  Kx ≡ (La • Lb) 
E)  None of the above. 
A)  Lb 
B)  La 
C)  La • Lb 
D)  Kx ≡ (La • Lb) 
E)  None of the above.

Question 15

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

Accepted Answer

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

Question 16

Translate each of the following sentences into predicate logic, using the given constants and predicates.
-Abhishek loves ice cream and pizza. (a: Abhishek; Ix: x loves ice cream; Px: x loves pizza)

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

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

Accepted Answer

A)  Hc • (Ic $ \lor $ Jc) 
B)  Ks ⊃ ∼Ix 
C)  Hx ⊃ Kw 
D)  Hx • (Ix $ \lor $ Jx) 
E)  Ha • (Ib $ \lor $ Jc) 
A)  Hc • (Ic $ \lor $ Jc) 
B)  Ks ⊃ ∼Ix 
C)  Hx ⊃ Kw 
D)  Hx • (Ix $ \lor $ Jx) 
E)  Ha • (Ib $ \lor $ Jc)

Question 19

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates.
-Some educated doctors are not gentle.

Accepted Answer

A)  (∃x) (Dx • Ex) 
B)  (∃x)[(Dx • Ex) • ∼Gx] 
C)  (∃x)[(Dx • Ex) ⊃ ∼Gx] 
D)  (∃x)[(Dx • Ex) • Gx] 
E)  (∃x) ∼[(Dx • Ex) ⊃ ∼Gx] 
A)  (∃x) (Dx • Ex) 
B)  (∃x)[(Dx • Ex) • ∼Gx] 
C)  (∃x)[(Dx • Ex) ⊃ ∼Gx] 
D)  (∃x)[(Dx • Ex) • Gx] 
E)  (∃x) ∼[(Dx • Ex) ⊃ ∼Gx]

Question 20

provide a conterexample in a finite domain to each given invalid argument.
-1. (∀x)(Mx ⊃ Nx)
2. (∃x)(Mx • Ox)
3. Oa / Oa • Na

Accepted Answer

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

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates. -No humans don't have a mother.

Things are pleasant if, and only if, they are not too crowded. Everything too crowded is noisy. So if something isn't noisy, then something is pleasant. -Which of the following is the best translation into M of this argument?

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

Translate each of the following sentences into predicate logic, using the given constants and predicates. -Kyrone has a thriving practice if Jalissa stops touring. (j: Jalissa; k: Kyrone; Px: x has a thriving practice; Tx: x stops touring)

select the best translation into predicate logic. -Not all the settlements have trading ports.

select the best translation into predicate logic. -Some tall athletes don't receive scholarships.

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

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 -If Tortuga is a city, then some settlements are not nicely placed.

refer to the following formula: (∃x)[Mx • (∼Nc $\lor$ ∼Ox)] ≡ (Py • Pb) -Which wffs below are not in the scope of '(∃x)'?

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates. -No red flowers are in the garden.

select the best translation into predicate logic. -Everyone is a theist unless someone is a skeptic and not an apriorist.

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 • Rx) • (Sx • Tx)]

refer to the following formula: (∀x)[(Ex $\lor$ Fx) ⊃ (Gx • Hd)] -Are there any free variables? If so, which are they?

refer to the following formula: ∼(∀x){(Ix • Jx) ⊃ [Kx ≡ (La • Lb)]} -Which wffs below are not in the scope of '(∀x)'?

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

Translate each of the following sentences into predicate logic, using the given constants and predicates. -Abhishek loves ice cream and pizza. (a: Abhishek; Ix: x loves ice cream; Px: x loves pizza)

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

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

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates. -Some educated doctors are not gentle.

provide a conterexample in a finite domain to each given invalid argument. -1. (∀x)(Mx ⊃ Nx) 2. (∃x)(Mx • Ox) 3. Oa / Oa • Na

Introducing Logic

Propositional Logic: Syntax and Semantic

Inference in Propositional Logic

Full First-Order Logic

Filters

Exam 4: Monadic Predicate Logic