Monadic Predicate Logic Translation Exercise II

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1. Some seniors are tall but Geoff, a senior, is not.

Ax: x is a senior

Bx: x is tall

a: Geoff

(∃x)(Ax & Bx) & (Aa & ~ Ba)

3. Not all green, moldy, round vegetables are tasty and nutritious.
 

Ax: x is green

Bx: x is moldy

Cx: x is round

Dx: x is a vegetable

Ex: x is tasty

Fx: x is nutritious

~(x)[(((Ax & Bx) & Cx) & Dx) ⊃ (Ex & Fx)]

5. Only discriminating eaters frequent cafeterias.

Ax: x is discriminating

Bx: x is an eater

Cx: x frequents cafeterias.

(x)(Cx ⊃ (Ax & Bx))

7.Some musicians are cool only if they play jazz.

Mx: x is a musician

Cx: x is cool

Jx: x plays jazz

(∃x)(Mx & (Cx ⊃  Jx)

9. No plumbers who make more than $250,000 are democrats.

Px: x is a plumber

Mx: x makes more than $250,000

Dx: x is a Democrat

(x)((Px & Mx) ⊃ ~ Dx)

11. It's not the case that some serious students spend every night in the library.

Ax: x is serious

Bx: x is a student

Cx: x spends every night in the library

(x)((Ax & Bx)  ⊃ ~Cx)

13. Any Oxy student who has taken logic can prove the functional completeness of PL.

Ox: x is an Oxy student

Lx: x has taken logic

Fx: x can prove the functional completeness of PL.

(x)((Ox & Lx) ⊃ Fx)

15. The only lazy people who didn't vote were the bicycle-riding philosophers.

Lx: x is lazy

Vx: x voted

Bx: x rides a bicycle

Px: x is a philosopher

(x)((Lx & ~Vx) ⊃  (Bx & Px))