Question 1

1. (∀x)(Cx ⊃ Dx)
2. (∀x)(Ex ⊃ ∼Dx)
-Which of the following propositions is derivable from the given premises in M?

Accepted Answer

A)  (∀x)(Ex ⊃ Cx) 
B)  (∀x)(Ex ⊃ ∼Cx) 
C)  (∃x)Ex 
D)  (∃x)Dx 
E)  (∀x)(∼Ex $ \lor $ Cx) 
A)  (∀x)(Ex ⊃ Cx) 
B)  (∀x)(Ex ⊃ ∼Cx) 
C)  (∃x)Ex 
D)  (∃x)Dx 
E)  (∀x)(∼Ex $ \lor $ Cx)

Question 2

Translate each of the following sentences into predicate logic, using the given constants and predicates.
-Some grass is high and thick. (Gx: x is grass; Hx: x is high; Tx: x is thick)

Accepted Answer

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

Question 3

select a counterexample for the given invalid argument.
-1. (∃x)(Mx • Nx)
2) (∀x)(Ox ⊃ Mx) / (∀x)(Ox ⊃ Nx)

Accepted Answer

A)  Counterexample in a domain of 2 members, in which:
Ma: True Na: True Oa: False
Mb: True Nb: True Ob: True 
B)  Counterexample in a domain of 2 members, in which:
Ma: True Na: False Oa: True
Mb: True Nb: True Ob: True 
C)  Counterexample in a domain of 2 members, in which:
Ma: True Na: False Oa: False
Mb: True Nb: False Ob: True 
D)  Counterexample in a domain of 2 members, in which:
Ma: True Na: False Oa: False
Mb: False Nb: True Ob: True 
E)  Counterexample in a domain of 2 members, in which:
Ma: False Na: False Oa: False
Mb: True Nb: True Ob: False 
A)  Counterexample in a domain of 2 members, in which:
Ma: True Na: True Oa: False
Mb: True Nb: True Ob: True 
B)  Counterexample in a domain of 2 members, in which:
Ma: True Na: False Oa: True
Mb: True Nb: True Ob: True 
C)  Counterexample in a domain of 2 members, in which:
Ma: True Na: False Oa: False
Mb: True Nb: False Ob: True 
D)  Counterexample in a domain of 2 members, in which:
Ma: True Na: False Oa: False
Mb: False Nb: True Ob: True 
E)  Counterexample in a domain of 2 members, in which:
Ma: False Na: False Oa: False
Mb: True Nb: True Ob: False

Question 4

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)(Fx ⊃ Gx)
2. (∃x)Fx / (∀x)(∼Gx ⊃ ∼Ex)

Accepted Answer

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

Question 5

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

Accepted Answer

The answer of refer to the following formula: ∼(∀x){(Ix •...

Question 6

∼(∃x)(Px • Qx) ≡ (∀x)(Px ⊃ ∼Qx)
-Which of the following propositions is also derivable in M given that same assumption?

Accepted Answer

A)  ∼Qx 
B)  ∼Pa $ \lor $ ∼Qa 
C)  Px 
D)  ∼Qx ⊃ Px 
E)  Pa • Qa 
A)  ∼Qx 
B)  ∼Pa $ \lor $ ∼Qa 
C)  Px 
D)  ∼Qx ⊃ Px 
E)  Pa • Qa

1. (∀x)(Cx ⊃ Dx) 2. (∀x)(Ex ⊃ ∼Dx) -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 grass is high and thick. (Gx: x is grass; Hx: x is high; Tx: x is thick)

select a counterexample for the given invalid argument. -1. (∃x)(Mx • Nx) 2) (∀x)(Ox ⊃ Mx) / (∀x)(Ox ⊃ Nx)

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)(Fx ⊃ Gx) 2. (∃x)Fx / (∀x)(∼Gx ⊃ ∼Ex)

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

∼(∃x)(Px • Qx) ≡ (∀x)(Px ⊃ ∼Qx) -Which of the following propositions is also derivable in M given that same assumption?

Introducing Logic

Propositional Logic: Syntax and Semantic

Inference in Propositional Logic

Full First-Order Logic

Filters

Exam 4: Monadic Predicate Logic