Polyadic Predicate Logic  Translation Exercise
Selected Answers

1.     Some non-philosophers hate every theorem

Px: x is a philosopher

Tx: x is a theorem

Hxy: x hates y

(∃x)(~Px & (y)(Ty ⊃ Hxy))

2.     Ignat is taller than every basketball player.

Txy: x is taller than y

Bx: x is a basketball player

a: Ignat

(x)(Bx  ⊃ Tax)

3.     The only good philosophers are those who are west of the Mississippi.

Gx: x is good

Px: x is a philosopher

Wxy: x is west of y

m: the Mississippi

(x)((Px & Gx)  ⊃ Wxm)

4.     Ignat doesn't like some people, but he does like Mathilda.

Px: x is a person

Lxy: x likes y

a: Ignat

b: Mathilda

(∃x)(Px & ~Lax) & Lab

5.     The Critique of Pure Reason is a harder book to read than A Treatise of Human Nature.

Hxy: x is harder to read than y

Bx: x is a book

a: The Critique of Pure Reason

b: A Treatise of Human Nature

((Ba & Bb) & Hab)

6.     Ignat recommended someone who is taller than Mathilda for a job.

Rxyz: x recommended y for z

Txy: x is taller than y

Jx: x is a job

a: Ignat

b: Mathilda

(∃z)(∃y)((Jz &Tyb) & Rayz )

7.     Anyone who runs with professional athletes will improve.

Px: x is a professional athlete

Rxy: x runs with y

Ix: x improves

(x)(y)((Py & Rxy) ⊃ Iy)

8.     No one who is friendlier than Ignat is taller than everyone.

Fxy: x is friendlier than y

Txy: x is taller than y

a: Ignat

(x)(y)(Fxa ⊃ ~Txy)

9.     Winter is colder than spring, summer or fall.

a:  winter

b: spring

c: summer

d:  fall

Cxy: x is colder than y

(Cab & Cac) & Cad

10. Some enchanted evening, Ignat will meet a stranger.

       Ax: x is enchanted
Bx: x is an evening
Sx: x is a stranger
Mxyz: x will meet y on z
a: Ignat

(∃x)((Ax & Bx) & (∃y)(Sy & Mayx))