I have a statement that I need to prove if it is a tautology or give a counter example if it is something else. The problem is there is not a lot of brackets in the whole thing and I can't be sure. I know that rules of precedence helps with these problems and tried that as well, but i can't be sure if I am doing something wrong. $$ p \Rightarrow \neg q \equiv (q \not\equiv r) \Rightarrow \neg p \equiv p \Rightarrow \neg r $$ I have tried my best to put brackets using the rules of precedence like this: $$ (p \Rightarrow (\neg q)) \equiv (q \not\equiv r) \Rightarrow (\neg p) \equiv (p \Rightarrow (\neg r)) $$
But then I don't know which part of the equation to try to reduce in order to prove it. Is that like this $$ ((p \Rightarrow (\neg q)) \equiv (q \not\equiv r)) \Rightarrow ((\neg p) \equiv (p \Rightarrow (\neg r))) $$ and should i try to take the last version as the statement and try to equate the antecedent$$ ((p \Rightarrow \neg q)) \equiv (q \not\equiv r)) $$ to the consequent? $$((\neg p) \equiv (p \Rightarrow (\neg r)) $$