Question 1

derive the conclusions of each of the following arguments using the rules of inference for F, including the rules for identity.
-1. (∃x)[Px • (∀y)(Py ⊃ y=x) • (∃y)(Qy • Rxy)]
2. (∃x)[Px • Sx • (∀y)∼Ryx] / (∃x)(∃y)(Rxy • ∼Ryx)

Accepted Answer

The answer of derive the conclusions of each of the...

Question 2

derive the conclusions of each of the following arguments using the rules of inference for F, including the rules for identity.
-1. Ha • (∀x)[(Hx • x≠a) ⊃ Jax]
2. Hb • Ib • Mb • (∀x)[(Ix • Mx) ⊃ x=b]
3. ∼Ma / Jab

Accepted Answer

The answer of derive the conclusions of each of the...

Question 3

derive the conclusions of each of the following arguments using the rules of inference for F, including the rules for identity.
-1. Ha • Ia • (?x)[(Hx • Ix) ? x=a]
2. Hb • Jb • (?x)[(Hx • Jx) ? x=b]
3. Ka • ?Kb / ?(?x)(Hx • Ix • Jx)

Accepted Answer

The answer of derive the conclusions of each of the...

Question 4

derive the conclusions of each of the following arguments using the rules of inference for F, including the rules for identity.
-1. (∀x)(Ecx ⊃ x=d)
2. (∀x){(Fx • Gx) ⊃ (∀y)[(Fy • Gy) ⊃ y=x]}
3. (∃x)(Fx • Gx • Ecx)
4. Fa • Ga / a=d

Accepted Answer

The answer of derive the conclusions of each of the...

Question 5

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)]

Accepted Answer

The answer of derive the conclusions of each of the...

Question 6

derive the conclusions of each of the following arguments using the rules of inference for F, including the rules for identity.
-1. (∃x)(∃y){Gx • Gy • x≠y • (∀z)[Gz ⊃ (z=x $ \lor $ z=y)]}
2. Ga • Gb • Gc / a=b $ \lor $ a=c $ \lor $ b=c

Accepted Answer

The answer of derive the conclusions of each of the...

Question 7

construct a derivation of each logical truth of identity theory.
-(?x)(?y)(Axy • x=y) ? (?x)Axx

Accepted Answer

The answer of construct a derivation of each logical truth...

Question 8

construct a derivation of each logical truth of identity theory.
-(?x)[Px • (?y)(Qy • y=x)] ? (?x)(Px • Qx)

Accepted Answer

The answer of construct a derivation of each logical truth...

Question 9

translate the given paragraphs into arguments written in F, using identity and the given translation key. Then, derive their conclusions using the rules of inference for F, including the rules for identity.
-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)

Accepted Answer

The answer of translate the given paragraphs into arguments written...

Question 10

translate the given paragraphs into arguments written in F, using identity and the given translation key. Then, derive their conclusions using the rules of inference for F, including the rules for identity.
-Rey received the highest grade on Test #1. Spencer, who is not Rey, received a grade on Test #1. So, Rey's grade is higher than Spencer's. (r: Rey; s: Spencer; t: Test #1; Gxy: x is a grade on y; Hxy: x is higher than y; Rxy: x received y)

Accepted Answer

The answer of translate the given paragraphs into arguments written...

Question 11

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
-Ahmed is Chloe's father and Delfia is Chloe's mother.

Accepted Answer