Advanced topics

*This part of the problem sheet is voluntary.

1. Show that if $\phi$ is tautologous, then any substitution instance of it is tautologous.
2. Show that if $\phi$ is inconsistent, then any substitution instance of it is inconsistent.
3. Show that if $\wedge$ and $\vee$ are the only truth-functor symbols occurring in $\phi$, then $\phi$ is contingent.
4. Specify a general recipe for constructing, given a number n, a sentence with logical notation which means `There are at least n frogs'.

Readings

(Hodges, 2001, §§25 (pp. 115-17 only), 34-36, 38)