Exam 4: Monadic Predicate Logic

Translate each of the following sentences into predicate logic, using the given constants and predicates. -Neither Gabriel nor Honoré play volleyball. (g: Gabriel; h: Honoré; Vx: x plays volleyball)

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

select the best translation into predicate logic. -No apriorist rationalists are skeptics, but Hume is.

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates. -Kyrone has a thriving practice if Jalissa stops touring.

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 are productive if and only if they are both nicely placed and not on the water.

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)(Jx ⊃ Kx) 2. ∼(∀x)Kx / ∼(∀x)Jx

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 -Tall athletes with determination either receive scholarships or play professional sports.

determine whether the given formula is a logical truth of M or not. If it is not a logical truth, select a false valuation. -[(∀x)(Fx ⊃ Gx) • (∀x)(Gx ⊃ Hx)] ⊃ (∃x)(Fx • Hx)

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)(Px • Qx) 2. (∃x)(Px • Rx) 3. (∀x)(Qx ⊃ Sx) 4. (∀x)(Rx ⊃ Tx) / (∃x)(Px • Sx) • (∃x)(Px • Tx)

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

translate the given paragraphs into arguments written in M, using the given translation key. Then, derive their conclusions using the rules of inference for M. -If some journalists are not respectable, then all journalists on the web have work to do. Some journalists on the web lack assignments. It is not the case that something without an assignment has work to do. So all journalists are respectable. (Ax: x has an assignment; Ix: x is on the web; Jx: x is a journalist; Rx: x is respectable; Wx: x has work to do)

show that the given formula is a logical truth of M, using the rules of inference including conditional or indirect proof. -∼(∃x)(Px • Qx) ≡ (∀x)(Px ⊃ ∼Qx)

use: b: Berkeley h: Hume Ax: x is an apriorist Cx: x is consistent Ex: x is an empiricist Ix: x is an idealist Px: x is a person Rx: x is a rationalist Sx: x is a skeptic Tx: x is a theist -Only consistent rationalists are apriorists.

select the best translation into predicate logic. -Some athletes play professional sports if, and only if, they have determination.

select the best English interpretation of the given statements of predicate logic. 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)]}

select a counterexample for the given invalid argument. -1. (∀x)[Tx ⊃ (∼Wx $\lor$ Fx)] 2) (∀x)[(∼Wx • Tx) ⊃ ∼Fx] 3) (∃x)(Tx • Fx) / (∃x)(Tx • ∼Wx)

select the best English interpretation of the given statements of predicate logic. 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) ⊃ (∃x)(Px • ∼Rx)

Translate each of the following sentences into predicate logic, using the given constants and predicates. -Efraim takes acting classes if, and only if, he gets time off from work. (e: Efraim; Ax: x takes acting classes; Wx: x gets time off from work)

Translate each of the following sentences into predicate logic, using the given constants and predicates. -No visitor stayed for dinner. (Sx: x stayed for dinner; Vx: x is a visitor)

If anything is stuck in traffic, Bruno will be mad if it is late. Something is neither annoyed nor not late. If Bruno is mad, then something is annoyed. So something is not stuck in traffic. -Which of the following is the best translation into M of this argument?