Exam 5: Full First-Order Logic

Translate each sentence into predicate logic, using the given translation keys. use: h: Hume l: Locke Px: x is a philosopher Rx: x is a rationalist Ixy: x influenced y Sxy: x is more skeptical than y -Hume is more skeptical than Locke.

The virtue ethicist who teaches Aristotle does not publish on moral theory. Smith is a virtue ethicist who teaches Aristotle. Either one publishes on moral theory or one publishes on applied ethics. So, Smith publishes on applied ethics. (s: Smith; Ax: x publishes on applied ethics; Mx: x publishes on moral theory; Tx: is teaches Aristotle; Vx: x is a virtue ethicist) -Which of the following is the best translation into F of this argument?

select the best translation into predicate logic, using the following translation key: b: Bhavin c: Chloe m: Megha n: Nietzsche p: Plato Ax: x is an altruist Jx: x is joyful Px: x is a philosopher Rx: x is Russian Tx: x is thoughtful Bxy: x is a brother of y Mxy: x mocks y Rxy: x is richer than y Sxy: x is smarter than y -Exactly three Russian philosophers are joyful.

use: b: Bhavin c: Chloe m: Megha n: Nietzsche p: Plato Ax: x is an altruist Jx: x is joyful Px: x is a philosopher Rx: x is Russian Tx: x is thoughtful Bxy: x is a brother of y Mxy: x mocks y Rxy: x is richer than y Sxy: x is smarter than y -Exactly three philosophers mock Plato and Nietzsche.

use the following translation key to write the sentences below in FF. a: Ahmed b: Bhavin c: Chloe d: Delfina e: Eduardo i: Irving f(x): the father of x g(x): the mother of x f(x,y): the only son of x and y Lxy: x loves y Sxy: x is a sister of y Txy: x teaches y -No one is the only son of Ahmed and Delfina.

select the best translation into predicate logic, using the following translation key: d: Diego s: Sean Dx: x is on the Dean's list Px: x is a philosophy major Sx: x is a student Vx: x is a valedictorian -At least four philosophy majors are on the Dean's list.

use the following translation key to write the sentences below in FF. a: Ahmed b: Bhavin c: Chloe d: Delfina e: Eduardo i: Irving f(x): the father of x g(x): the mother of x f(x,y): the only son of x and y Lxy: x loves y Sxy: x is a sister of y Txy: x teaches y -Irving's father teaches Bhavin and Eduardo.

1. (∀x)(∀y)(∃z)Sf(x)yz 2. (∀x)(∀y)(∀z)[Sxyz ⊃ ∼(Cxyz $\lor$ Mzyx)] / (∃x)(∃y)(∃z)∼Mzg(y)f(g(x))

select the best translation into predicate logic, using the following translation key: b: Bhavin c: Chloe m: Megha n: Nietzsche p: Plato Ax: x is an altruist Jx: x is joyful Px: x is a philosopher Rx: x is Russian Tx: x is thoughtful Bxy: x is a brother of y Mxy: x mocks y Rxy: x is richer than y Sxy: x is smarter than y -There are at most two Russian altruists.

use: b: Britain c: Charles e: Elizabeth t: Tescos Px: x is a person Qx: x is a Queen of England Wx: x is a woman Exy: x is more exalted than y Ixy: x is in y Pxy: x shops at y Sxy: x is a son of y -No one who shops at Tescos is more exalted than Charles.

select the best translation into predicate logic, using the following translation key: a: Ahmed b: Bhavin c: Chloe d: Delfina e: Eduardo i: Irving f(x): the father of x g(x): the mother of x f(x,y): the only son of x and y Lxy: x loves y Sxy: x is a sister of y Txy: x teaches y -Bhavin's paternal grandparents love each other.

determine whether the given argument is valid or invalid. If it is invalid, select a counterexample. -1. (∀x)(Ax ⊃ Dex) 2) (∃x)(Bx • Dxe) 3) (∀x)(Bx ⊃ Ax) / (∃x)[Ax • (Dxe • Dex)]

select the best translation into predicate logic, using the following translation key: d: Diego s: Sean Dx: x is on the Dean's list Px: x is a philosophy major Sx: x is a student Vx: x is a valedictorian -Of the philosophy majors, only Diego is a valedictorian.

derive the conclusions of each of the following arguments using the rules of inference for F, including the rules for identity. -1. (∀x)(∀y)(∀z)[(Ix • Jx • Iy • Jy • Iz • Jz) ⊃ (x=y $\lor$ y=z $\lor$ x=z)] 2. Ia • Ja • Ka • Ib • Jb • Kb • a≠b / (∀x)[(Ix • Lx) ⊃ (x=a $\lor$ x=b $\lor$ ∼Jx)]

use: b: Britain c: Charles e: Elizabeth t: Tescos Px: x is a person Qx: x is a Queen of England Wx: x is a woman Exy: x is more exalted than y Ixy: x is in y Pxy: x shops at y Sxy: x is a son of y -All people in Britain shop at Tescos, except Elizabeth.

use: d: Diego s: Sean Dx: x is on the Dean's list Px: x is a philosophy major Sx: x is a student Vx: x is a valedictorian -Only Sean and Diego are both on the Dean's list and philosophy majors.

derive the conclusions of each of the following arguments using the rules of inference for F. -1. (∀x)[(Cx • Exa) ⊃ Dx] 2. Cd • ∼Dd / ∼Eda

1. (∃x)(Ax • Bx • Cax) 2. (∀x)[(Ax • Cax) ⊃ x=d] -Which of the following propositions is an immediate (one-step) consequence in F of the given premises?

All cheetahs are faster than some tigers. Everything is striped if, and only if, it is a tiger. So, if some things are cheetahs, then some things have stripes. (Cx: x is a cheetah; Tx: x is a tiger; Sx: x has stripes; Fxy: x is faster than y) -Which of the following is the best translation into F of this argument?

use the following translation key to write the sentences below in FF. a: Ahmed b: Bhavin c: Chloe d: Delfina e: Eduardo i: Irving f(x): the father of x g(x): the mother of x f(x,y): the only son of x and y Lxy: x loves y Sxy: x is a sister of y Txy: x teaches y -If anyone teaches the only son of Chloe and Eduardo, then someone teaches both Irving and Bhavin.