Exam 4: Monadic Predicate Logic

derive the conclusions of each of the following arguments using the rules of inference for M, including conditional or indirect proof. -1. (∀x)Ix $\lor$ ∼(∃x)Hx 2. (∃x)Jx ⊃ ∼(∀x)Ix 3. Hc / (∀x)∼Jx

refer to the following formula: (∃x)[Mx • (∼Nc $\lor$ ∼Ox)] ≡ (Py • Pb) -Which variables are bound by the '(∃x)'?

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 3. ∼(∀x)Ix $\lor$ (∀x)Jx / (∃x)∼Ix

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 -No athletes who play professional sports and have determination are neither tall nor work hard.

refer to the following formula: (∃x)[(Ax • ∼Bx) • ∼(Cx $\lor$ Dx)] -List all of the subformulas in the scope of '(∃x)'.

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} -(∀x)[Ax ⊃ (Bx $\lor$ Cx)] Aa Bb Cc

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

Translate each of the following sentences into predicate logic, using the given constants and predicates. -Some visitors did not stay for dinner. (Sx: x stayed for dinner; Vx: x is a visitor)

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates. -Neither Gabriel nor Honoré play volleyball.

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} -(∃x)(Ax • ∼Bx) ⊃ (∃x)(Ax • Bx) ∼(∃x)(Cx • Bx) (∀x)(Cx ⊃ Ax)

select the best translation into predicate logic. -Some settlements are not on the water.

1. (∀x)(Ax ⊃ Bx) 2. (∃x)Ax 3. (∃x)Bx ⊃ (∃x)Dx -Which of the following propositions is derivable from the given premises in M?

1. (∀x)(Jx ⊃ Kx) 2. ∼(∀x)Kx 3. ∼(∀x)Ix $\lor$ (∀x)Jx -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)Ax 2. (∀x)∼Ax ⊃ ∼(∃x)Bx / Ba

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 • Rx) • (Sx • Tx)]

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 can also be proved from the premises of the above argument?

derive the conclusions of each of the following arguments using the rules of inference for M, including conditional or indirect proof. -1. (∀x)(Px ⊃ Qx) 2. ∼(∃x)[(Px • Rx) • Qx] 3. (∃x)Rx / ∼(∀x)Px

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 -Not all the settlements have trading ports.

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)] ⊃ (∀x)[(Px • Rx) ⊃ Tx)]

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)(Mx • Ox) ⊃ (∃x)Nx 2. (∃x)(Px • Mx) 3. (∀x)(∼Px $\lor$ Ox) / (∃x)Nx