Monadic Predicate Logic Translation Exercise I

Selected Answers

1. Some terrible tantrums are unbearable.

Ax: x is terrible

Bx: x is is a tantrum

Cx: x is bearable.

(∃x)((Ax & Bx) & ~Cx)

3. No students are registered unless they go to the library.
 

Ax: x is a student

Bx: x is registered

Cx: x goes to the library

(x)((Ax ⊃  (~Bx v Cx))
 

5. Not all tall buildings are unsafe in earthquakes.
 

Ax: x is tall

Bx: x is a building

Cx: x is safe in earthquakes

(∃x)((Ax & Bx) & ~~Cx)

7. Unless everyone wears black, all funerals will be a farce.

Bx: x wears black

Fx: x is a funeral

Gx: x is a farce

(x)(Bx v (Fx ⊃  Gx)

9. Students who are vegans get good grades.

Sx: x is a student

Vx: x is a vegan

Gx: x gets good grades

(x)((Sx & Vx) ⊃ Gx)

11. Both Republicans and Democrats will vote for the peace treaty, unless Trump gets angry.

Rx: x is a Republican

Dx: x is a Democrat

Vx: x will vote for the peace treaty

Ax: x gets angry

a: Trump

(x)((Rx v Dx) ⊃ Vx) v Aa

13. Anyone would appeal unless they were afraid of losing.

Ax: x would appeal

Lx: x is afraid of losing

(x)(~Lx ⊃ Ax)