Translating Numerical Propositions - Selected Solutions

1, There is at least one moon.

Mx: x is a moon.

(∃x)Mx

2. There is at most one moon.

(x)((Mx ⊃ (y)(My  ⊃ x = y))

3. There are two moons.

(∃x)(∃y)(Mx & My & x ≠ y &  (z)(Mz ⊃  (z = x) v (z = y))

5. Blanche owns at least one pen.

a: Blanche

Px: x is a pen

Oxy: x owns y

(∃y)(Py & Oay)

6. Blanche owns exactly one pen.

(∃y)((Py & Oay) & (z)((Pz & Oay) ⊃ z = y)

7. Solomon fixed at most two tires.

s: Solomon

Fxy: x fixed y

Tx: x is a tire

(x)(y)(((Tx & Ty) & (z)(Tz ⊃ (z=x v z=y)) ⊃ (Fsx & Fsy))