In Cresswell and Hughes: "A new introduction to Modal Logic" they in question 2.4 ask to show that $L(M(\alpha))$ isn't a theorem of $K$ system (where L is the necessary operator and M the possible operator).
Here's what I thought, I can substitute $\alpha$ for p&~p
So I get:
L(M(p&~p)) assumption ad absurdum.
L(Mp & M~p) 1, K8+N+K+MP
LM(p) & LM(~p) 2, K3.
Here's where I got stuck, and I am not sure how to deduce a contradiction.
Any hints or thoughts?
Thanks in advance.