Exam 4: Monadic Predicate Logic

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 ⊃ (∼Sx ⊃ Tx)]}

1. ∼(∃x)Ax 2. (∀x)∼Ax ⊃ ∼(∃x)Bx -Which of the following propositions is an immediate (one-step) consequence in M of the given premises?

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

refer to the following formula: ∼(∀x){(Ix • Jx) ⊃ [Kx ≡ (La • Lb)]} -Which is the main operator of the formula?

select the best translation into predicate logic. -Some rationalists who are skeptics are not theists.

refer to the following formula: (∀x)[(Ex $\lor$ Fx) ⊃ (Gx • Hd)] -List all of the subformulas in the scope of '(∀x)'.

determine whether the given argument is valid or invalid. If it is invalid, select a counterexample. -1. (∃x)(Px • Qx) 2) (∃x)(Px • Rx) 3) (∀x)(Qx ⊃ Sx) 4) (∀x)(Rx ⊃ Tx) / (∃x)(Px • Sx) • (∃x)(Px • Tx)

select the best translation into predicate logic. -Some athletes who don't work hard receive scholarships, if, and only if, no athletes who play professional sports don't have determination.

construct a model for each of the given theories in the following domain by assigning members of the domain to the constants used in the theory and sets of members of the domain to the predicates used in the theory. Domain = {Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune} -Aa • Ab ∼Ba • ∼Bb (∃x)(Ax • Bx)

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates. -Some grass is high and thick.

1. (∃x)(Mx • Ox) ⊃ (∃x)Nx 2. (∃x)(Px • Mx) 3. (∀x)(∼Px $\lor$ Ox) -Which of the following propositions is derivable from the given premises in M?

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 propositions is a good assumption for conditional proof for the above argument?

1. (∃x)(Gx • ∼Hx) ≡ (∃x)(Hx • ∼Ix) 2. (∀x)(Hx ⊃ Ix) -Which of the following propositions is derivable from the given premises in M?

select the best translation into predicate logic. -All cities are productive if and only if they are both nicely placed and not on the water.

(∃x)(Px • Qx) ⊃ [(∃x)Px • (∃x)Qx] -Consider assuming '(∃x)(Px • Qx)' for a conditional proof of the above logical truth. Which Of the following propositions is a legitimate second step in that proof?

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?

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)(Cx ⊃ Dx) 2. (∀x)(Ex ⊃ ∼Dx) / (∀x)(Ex ⊃ ∼Cx)

Some materialist empiricists are either libertarians or hard determinists. But no empiricist is a hard determinist. So some materialists are libertarians. -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. -No visitor stayed for dinner.

1. (∀x)(Jx ⊃ Kx) 2. (∀x)(Jx ⊃ ∼Lx) -Consider assuming 'Jx' 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?