Phi 270 F96 test 4

F96 test 4 questions

(Questions 1-3 are from quiz 4 and 4-9 are from quiz 5 out of 6 quizzes—these two quizzes addressed the part of the course your test is designed to cover.)

Identify individual terms and quantifier phrases in the following sentence and indicate links between pronouns and their antecedents. (You can do this by marking up an English sentence; you are not being asked to provide a symbolic analysis.)

1. Al called everyone who left him a message concerning the accident and told them he had seen it.
answer

Analyze the following generalizations in as much detail as possible. Provide a key to the non-logical vocabulary (upper and lower case letters) appearing in your answer and restate the result using an unrestricted quantifier.

2. Every employee received the letter.
answer
3. Among bystanders, Sam interviewed only soldiers.
answer

Analyze the following sentences in as much detail as possible, providing a key to the non-logical vocabulary (upper and lower case letters) appearing in your answer.

4. If anyone guessed the number, the prize was awarded.
answer
5. Everyone who worked on any part of the project was honored.
answer

Synthesize an English sentence whose analysis would yield the following form.

6. (∀x: Px) ¬ ∀y Axy
A: [ _ ate _ ]; P: [ _ is a person]
answer

Use derivations to establish the validity of the following arguments. You may use attachment rules.

7.
∀x Fx
∀x Gx
∀x (Fx ∧ Gx)
answer 		8.
∀x (Fx → Rxa)
∀x (Rxa → ∀y Ryx)
∀x ∀y (Fy → Rxy)
answer

Use a derivation to show that the following argument is not valid and describe a counterexample lurking in one of the derivation’s open gaps. (You will not need the rules UG+ and ST introduced in §7.8 that are designed to avoid unending gaps.)

9.
∀x Rxx
Rab → ∀x Rxa
answer

F96 test 4 answers

1.

[it could instead have a message concerning the accident as its antecedent]

2.

Every employee received the letter

Every employee is such that (he or she received the letter)

(∀x: x is an employee) x received the letter

(∀x: Ex) Rxl
∀x (Ex → Rxl)

E: [ _ is an employee]; R: [ _ received _ ]; l: the letter

3.

Among bystanders, Sam interviewed only soldiers

Among bystanders, only soldiers are such that (Sam interviewed them)

(∀x: x was a bystander ∧ ¬ x was a soldier) ¬ Sam interviewed x

(∀x: Bx ∧ ¬ Sx) ¬ Isx
∀x ((Bx ∧ ¬ Sx) → ¬ Isx)

B: [ _ was a bystander]; I: [ _ interviewed _ ]; S: [ _ was a soldier]; s: Sam

4.

If anyone guessed the number, the prize was awarded

Everyone is such that (if he or she guessed the number, the prize was awarded)

(∀x: x is a person) (if x guessed the number, the prize was awarded)

(∀x: Px) (x guessed the number → the prize was awarded)

(∀x: Px) (Gxn → Ap)

P: [ _ is a person]; G: [ _ guessed _ ]; n: the number

5.

Everyone who worked on any part of the project was honored

Every part of the project is such that (everyone who worked on it was honored)

(∀x: x is a part of the project) everyone who worked on x was honored

(∀x: Rxj) (∀y: y is a person who worked on x) y was honored

(∀x: Rxj) (∀y: y is a person ∧ y worked on x) Hy

(∀x: Rxj) (∀y: Py ∧ Wyx) Hy

H: [ _ was honored]; P: [ _ is a person]; R: [ _ is a part of _ ]; W: [ _ worked on _ ]; j: the project

6.

(∀x: x is a person) ¬ ∀y x ate y

(∀x: x is a person) ¬ x ate everything

No one is such that (he or she ate everything)

No one ate everything

7.
│∀x Fx a:2
│∀x Gx a:3
├─
│ⓐ 
2 UI ││Fa (5)
3 UI ││Ga (6)
││
│││●
││├─
5 QED │││Fa 4
││
│││●
││├─
6 QED │││Ga 4
│├─
4 Cnj ││Fa ∧ Ga 1
├─
1 UG │∀x (Fx ∧ Gx) 1
8.
│∀x (Fx → Rxa) c:4
│∀x (Rxa → ∀y Ryx) c:6
├─
│ⓑ
││ⓒ
││││Fc (5)
│││├─
4 UI ││││Fc → Rca 5
5 MPP ││││Rca (7)
6 UI ││││Rca → ∀y Ryc 7
7 MPP ││││∀y Ryc b:8
8 UI ││││Rbc (9)
││││●
│││├─
9 QED ││││Rbc 3
││├─
3 CP │││Fc → Rbc 2
│├─
2 UG ││∀y (Fy → Rby) 1
├─
1 UG │∀x ∀y (Fy → Rxy)
9.
│∀x Rxx a:1,b:2,c:5
├─
1 UI │Raa
2 UI │Rbb
│
││Rab
│├─
││ⓒ
5 UI │││Rcc
│││
││││ ¬ Rca
│││├─
││││ ○ Raa,Rab,Rbb,Rcc,¬Rca ⊭ ⊥
│││├─
││││⊥ 6
││├─
6 IP │││Rca 4
│├─
4 UG ││∀x Rxa 3
├─
3 CP │Rab → ∀x Rxa