Exam 4: Monadic Predicate Logic

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

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 -All cities and settlements are nicely placed and productive.

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

Some websites have open comments which are not anonymous. Any website is either anonymous or requires a login. So something with open comments requires a login. -Which of the following claims can also be derived from the premises of this argument?

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?

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

provide a conterexample in a finite domain to each given invalid argument. -1. (∀x)(Kx ⊃ ∼Lx) 2. (∃x)(Mx • Lx) / (∀x)(Kx ⊃ ∼Mx)

1. (∀x)[(Px $\lor$ Qx) ⊃ (Rx • ∼Sx)] 2. (∀x)[Rx ⊃ (Tx ⊃ ∼Sx)] -Consider assuming 'Px' 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?

Translate each of the following sentences into predicate logic, using the given constants and predicates. -Izzy takes linear algebra only if she does not take discrete mathematics. (i: Izzy; Dx: x takes discrete mathematics; Lx: x takes linear algebra)

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

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)(Ax ⊃ Bx) 2. (∃x)Ax 3. (∃x)Bx ⊃ (∃x)Dx / (∃x)Dx

determine whether the given formula is a logical truth of M or not. If it is a logical truth, provide a proof of the formula. If it is not a logical truth, provide a counterexample in a finite domain. -(∃x)(Ix • Jx) ⊃ [(∀x)Ix ⊃ (∀x)Jx]

1. ∼(∃x)[Fx • (Gx • Hx)] 2. ∼(∃x)(Ix • ∼Fx) -Which of the following propositions is an immediate (one-step) consequence in M of the given premises?

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)(Kx $\lor$ Lx) 2. (∀x)(Jx ⊃ ~Lx) / (∃x)(~Jx $\lor$ Kx)

provide a conterexample in a finite domain to each given invalid argument. -1. (∃x)(Hx • Ix) 2. (∃x)(Hx • ∼Ix) 3. (∀x)(Jx ⊃ Ix) / (∀x)(Jx ⊃ Hx)

Translate each sentence into predicate logic, using the given translation keys. Ax: x is an athlete Dx: x has determination Px: x plays professional sports Sx: x receives a scholarship Tx: x is tall Wx: x works hard -All tall athletes work hard.

Everything is material, or ideal or transcendental. All atoms are not ideal and not transcendental. And nothing is material. So there are no atoms. -Which of the following propositions is a good assumption for indirect proof for the above argument?

Translate each of the following sentences into predicate logic, using the given constants and predicates. -All mammals feed their young. (Fx: x feeds their young; Mx: x is a mammal)

Translate each of the following sentences into predicate logic, using the given constants and predicates. -If Carla works for an airline, then Darlene doesn't. (c: Carla; d: Darlene; Ax: x works for an airline)

select the best translation into predicate logic. -Only tall athletes play professional basketball.