Phi 270 F98 part of quiz 4 and all of quiz 5 (of 6) in pdf format
(questions from these two tests addressed the part of the course your test is designed to cover)
4-5. 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.)
Sam ordered a book, but instead of it he received a book he didn't want.
[answer]
4-6. Analyze the following generalization in as much detail as possible. Provide a key to the non-logical vocabulary (upper and lower case letters) appearing in your answer.
  No one saw the book that was lying on the table.
[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.
5-1. No one except numismatists understood the joke
[answer]
5-2. The movie delighted all boys and girls
[answer]
5-3. If anyone relayed the message to everyone, then no one understood every part of it
[answer]
Use derivations to establish the validity of the following arguments. You may use attachment rules.
5-4.
∀x (Fx ∨ Gx)
∀x ¬ Gx
∀x Fx
[answer]
5-5.
(∀x: Fx) (∀y: Pxy) Rxy
∀y (∀x: Fx ∧ Pxy) Rxy
[answer]
5-6. Use a derivation to show that the following argument is not valid and describe a structure dividing one of the derivation's open gaps.
(∀x: Fx) ¬ Rxx
∀x (∀y: Fy) ¬ Rxy
[answer]
Phi 270 F98 Answers to part of quiz 4 and all of quiz 5
4-5.
      
              
Samorderedabook, but instead ofit he received a bookhedidn't want
                
T Q       Q  
4-6. No one saw the book that was lying on the table.
No one is such that (he or she saw the book that was lying on the table)
(∀x: x is a person) ¬ x saw the book that was lying on the table
(∀x: Px) ¬ Sx(the book that was lying on the table)
(∀x: Px) ¬ Sx(bt)
[P: λx (x is a person); S: λxy (x saw y); b: λx (the book that was lying on x); t: the table]
   
5-1.

No one except numismatists understood the joke

(∀x: x is a person ∧ ¬ x is a numismatist) ¬ x understood the joke

(∀x: Px ∧ ¬ Nx) ¬ Uxj
[N: λx (x is a person); P: λx (x is a numismatist); U: λxy (x understood y); j: the joke]
5-2.

The movie delighted all boys and girls

all boys and girls are such that (the movie delighted them)

(∀x: x is a boy or girl) the movie delighted x

(∀x: x is a boy ∨ x is a girl) the movie delighted x

(∀x: Bx ∨ Gx) Dmx
[B: λx (x is a boy); D: λxy (x delighted y); G: λx (x is a girl); m: the movie]
5-3.

If anyone relayed the message to everyone, then no one understood every part of it

(∀x: x is a person) if x relayed the message to everyone, then no one understood every part of it

(∀x: Px) (x relayed the message to everyone → no one understood every part of the message)

(∀x: Px) ((∀y: y is a person) x relayed the message to y → (∀z: z is a person) ¬ z understood every part of the message)

(∀x: Px) ((∀y: Py) x relayed the message to y → (∀z: Pz) ¬ (∀w: w is a part of the message) z understood w)

(∀x: Px) ((∀y: Py) Rxmy → (∀z: Pz) ¬ (∀w: Twm) Uzw)
[P: λx (x is a person); R: λxyz (x relayed y to z); T: λxy (x is a part of y); U: λxy (x understood y); m: the message]
5-4.
│∀x (Fx ∨ Gx) a:2
│∀x ¬ Gx a:3
├─
│ⓐ
2 UI ││Fa ∨ Ga 4
3 UI ││¬ Ga (4)
4 MTP ││Fa (5)
││●
│├─
5 QED ││Fa 1
├─
1 UG │∀x Fx
5-5.
│(∀x: Fx) (∀y: Pxy) Rxy b:4
├─
│ⓐ
││ⓑ
│││Fb ∧ Pba 3
││├─
3 Ext │││Fb (4)
3 Ext │││Pba (5)
4 SB │││(∀y: Pby) Rby a:5
5 SB │││Rba (6)
│││●
││├─
6 QED │││Rba 2
│├─
2 RIG ││(∀x: Fx ∧ Pxa) Rxa 1
├─
1 UG │∀y (∀x: Fx ∧ Pxy) Rxy
5-6.
│(∀x: Fx) ¬ Rxx b:4,a:5
├─
│ⓐ
││ⓑ
│││Fb (4)
││├─
││││Rab
│││├─
4 SB ││││¬ Rbb
││││
││││││¬ Fa
│││││├─
││││││○ Fb,Rab,¬Rbb,¬Fa ⇏ ⊥
│││││├─
││││││⊥ 6
││││├─
6 IP │││││Fa 5
││││
│││││¬ Raa
││││├─
│││││○ Fb,Rab,¬Rbb,¬Raa ⇏ ⊥
││││├─
│││││⊥ 5
│││├─
5 MCR ││││⊥ 3
││├─
3 RAA │││¬ Rab 2
│├─
2 RUG ││(∀y: Fy) ¬ Ray 1
├─
1 UG │∀x (∀y: Fy) ¬ Rxy
This structure divides both gaps: