Exam 4: Monadic Predicate Logic

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)(Jx • ∼Kx) ⊃ (∃x)(Lx • Mx) 2. (∃x)(Jx • Lx) 3. ∼(∃x)(Jx • Kx) / ∼(∀x)(Lx ⊃ ∼Mx)

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

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 -Berkeley is an empiricist and Hume is not an apriorist.

derive the conclusions of each of the following arguments using the rules of inference for M, including conditional or indirect proof. -1. (∀x)(Jx ⊃ Kx) 2. (∀x)(Jx ⊃ ∼Lx) / (∀x)[Jx ⊃ (Kx • ∼Lx)]

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 -All idealists are apriorists, but not theists.

select a counterexample for the given invalid argument. -1. (∃x)(∼Ax ≡ Cx) 2) (∃x)(Ax • Cx) 3) (∀x)(Bx ⊃ Ax) / (∀x)(Cx ⊃ Bx)

provide a conterexample in a finite domain to each given invalid argument. -1. (∃x)Sx 2. (∀x)[Sx ⊃ (Tx ⊃ ∼Ux)] 3. Ua • Ub 4. (∃x)∼Ux / (∃x)(Sx • ∼Tx)

Translate each of the following sentences into predicate logic, using the given constants and predicates. -Some cherries are red. (Cx: x is a cherry; Rx: x is red)

refer to the following formula: (∃x)[Mx • (∼Nc $\lor$ ∼Ox)] ≡ (Py • Pb) -What is the main operator of the given formula?

refer to the following formula: (∀x)[(Ex $\lor$ Fx) ⊃ (Gx • Hd)] -Which wffs below are not in the scope of '(∀x)'?

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)[Ax • (Bx $\lor$ Cx)] 2. (∀x)(Bx ⊃ ∼Cx) 3. (∃x)Bx 4. Ca / (∃x)(Ax • Cx)

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates. -Izzy takes linear algebra only if she does not take discrete mathematics.

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates. -Bonita doesn't study law; she's pre-med.

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates. -Farzona's dropping art history is a sufficient condition for her being unhappy.

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

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 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. -Some visitors did not stay for dinner.

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) ⊃ (∃x)(Px • ∼Rx)

Translate each of the following sentences into predicate logic, using the given constants and predicates. -No humans don't have a mother. (Hx: x is a human; Mx: x has a mother)

refer to the following formula: (∃x)[(Ax • ∼Bx) • ∼(Cx $\lor$ Dx)] -Which of the following variables in the formula are free?