For each of the following expressions of PL, determine (1) is it a formula? (2) is it a sentence? (3) list all of the sub-formulas and their type.

1. Ja v (x)Jx
2. (x) Hx -> ~Gx
3. ~ (y) [Ly -> (z) Bzy

Show that the following sentences of PL are not quantificationally true.

1. (y) (Ly -> Hy) -> (y) ~Ly
2. (z) Hz -> ~(y) (Ky -> Hy)

Show that the following sentences of PL are not quantificationally false.

1. (y)[ My -> (Ny & Ly)]
2. Ra -> (x) Sx

Show that the following sentence of PL is quantificationally indeterminate.

1. (y)(z) [Nyz -> ~Nzy]