Axiom 1: p ->~y
Axiom 2: ~q ->r
Theorem 1: p -> ~z
Theorem 2: x -> either q or z
Theorem 3: r -> either x or y
Write a two-column proof of the proposition p -> q
Axiom 1: p ->~y
Axiom 2: ~q ->r
Theorem 1: p -> ~z
Theorem 2: x -> either q or z
Theorem 3: r -> either x or y
Write a two-column proof of the proposition p -> q
This is as far as I can get:
Assume p.
It follow from (Axiom 1) that ~y.
It follows from (Thrm. 1) that ~z.
Are you sure you copied down the Axioms and Theorems correctly?
If we also assumed ~x, then
it follows from (Thrm. 3) that ~r.
Finally it follows from (Axiom 2) that q.
Therefor, (p and ~x) -> q
Q.E.D.?