Superlatives and Exceptives - Selected Solutions

1. Every Oxy student except Ignat loves logic.

Sxy: x is a student at y

a: Oxy

b: Ignat

Lxy: x loves y

My: y is logic

(x)(y)(((Sxa & x ≠ b) & My) ⊃Lxy)) & Sba

2. Joe Pass is the greatest guitarist.

a: Joe Pass

Gx: x is a guitarist.

Bxy: x is better than y.

(x)(((Gx & x ≠ a)) ⊃ Bax) & Ga

3. The Internet is the most popular network.

a: The Internet

Pxy: x is more popular than y

Nx: x is a network

(x)((Nx & x ≠ a) ⊃ Pax) & Na

4. The tallest person on the planet is also the fastest.

Txy: x is taller than y

Fxy: x is faster than y

Px: x is a person

Oxy: x is on y

e: Earth

(∃x)(y)(((Px & Oxe) & (Py & Oye)) &  (Txy &  Fxy)) & (z)((Pz & Oze) ⊃  ((Tzy &  Fzy) ⊃ z = x))

(Note: Here I've translated "the planet" as "Earth".)

5. Everyone except Ignat passed the final.

a: Ignat

Pxy: x passed y

Fx: x is a final

(∃x) ((Fx & (y)(Fy ⊃ y=x)) & (z)((z ≠a) ⊃ Pzx) & ~Pax)

6. The only person hungrier than Bethsheba is Gabriel.

b: Bethsheba

g: Gabriel

Px: x is a person

Hxy: x is hungrier than y

(x)((Px & Hxb) ⊃ x=g) & (Pg & Hgb)

7. No one plays sax like Cannonball.

c: Cannonball

Pxyz: x plays y like z

Sx: x is a sax

~(∃x)(y)((Sy & Pxyc) & x=c)  & Pcyc)

Can you form the E categorical version?

8. Desperate Remedies is Hardy's earliest novel.

a: Desperate Remedies

b: Hardy

Nx: x is a novel

Exy: x is earlier than y

Wxy: x wrote y

(x)((Nx & Wbx) & x ≠ a ⊃ Eax) & (Na & Wba)

9. The only jazz pianist in the room owns a Yamaha.

Yx: x is a Yamaha.

Jx: x is a jazz pianist

Oxy: x owns y

(x)(y)((((Jx & Rx) & Yy) ⊃ Oxy) & (z)((((Jz &Rz) & Yz) ⊃ Ozy) ⊃ z=x)))

10. Formal Logic is the most challenging course at Oxy.

f: formal logic

o: Oxy

Bx: x is a course

Cxy: x is more challenging than y.

Axy: x is offered at y

(x)(((Bx& Axo) & x ≠ f) ⊃Cfx)  & (Bf & Afo))