q
r, q
r, since soundness of
propositional logic would then imply that p
q
r, q
r holds as
well. But the latter is not true (recall Question 5); for if r is false, q is
true, and p is false, then p
q
r and q are true,
but the claimed consequence, r, is not.
However, can you prove the weaker sequent
p, p
q
r, q
r?