logical equivalence question about contingency I want to know if these are two acceptable ways of reaching the same answer or is the first incorrect? Thanks $$p \rightarrow (p \vee q) \equiv \neg p \vee (p \vee q) \equiv (\neg p \vee p) \vee q $$ $$\equiv \text{true} \wedge q \equiv q = \text{contingency} $$ $$p \rightarrow (p \vee q) \equiv \neg p \vee (p \vee q) \equiv (\neg p \vee p) \wedge (\neg p \vee q) $$ $$\equiv \text{true} \wedge p \rightarrow q \equiv p \rightarrow q = \text{contingency}$$

The first is correct, the second is not. Association is the right rule to use; distribution is not applicable--distribution does not work like that.