7.1ex I

Think about the following interpretation:


universe of discourse = all inner planets of our solar system, Earth, Mars, Venus, Mercury.

a: Mercury, b: Venus, c: Earth, d: Mars,

Sx: "x has a natural satellite (a moon)."
I.e., 'Sc' and 'Sd' are true as 'S' is associated only with the planets having moons: Earth (c) and Mars (d).
Tx: "x is a terrestrial (rocky) planet".
I.e. 'Sa','Sb','Sc', and 'Sd' are all true because the inner planets (unlike the outer ones) are terrestrial as opposed to gassy or icy.
Ixy: "x orbits inside y".
So, for examples, 'Iab' is true: Mercury orbits inside Venus. So are: 'Iac',Iad','Ibc','Ibd',and 'Icd'.
Now consider the sentence,

(*) (^x)[(Sx&Tx)>Ixd].

What does it mean for (*) to be true?

  1. Each substitution instance of (*) is true.
  2. Exactly one substitution instance of (*) is true.
  3. At least one substitution instance of (*) is true