Can't get Logical Error

Question

Firstly I 'll mention Absorption laws :

1. $((\sim p) \vee q) \wedge (\sim q)=(\sim p)$
   $((\sim p) \vee q) \wedge p=q$

Also, $p \Longrightarrow q = (\sim p) \vee q$

And, $p \Longleftrightarrow q = (p \Longrightarrow q) \wedge (q \Longrightarrow p)$

Let we have $p \Longrightarrow q = (\sim p) \vee q$
Now, given two absorption laws above, we have $p \Longrightarrow q = [((\sim p) \vee q) \wedge (\sim q)] \vee [(\sim p) \vee q) \wedge p]= [(\sim p) \vee q] \wedge [(\sim q) \vee p]$ So, This expression becomes $p \Longrightarrow q = p \Longleftrightarrow q.$

Where I'm mistaken ?

Answer 1

Correction

Applying Distribution to : $(\lnot p∨q)∧\lnot q$ we get :

$(\lnot p \land \lnot q) \lor (q \land \lnot q) \equiv (\lnot p \land \lnot q) \lor F \equiv (\lnot p \land \lnot q).$

In the same way :

$(\lnot p ∨ q)∧p \equiv (p \land q)$.

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Absorption is :

$(\lnot p \lor q) \equiv (\lnot p \lor (p \land q))$.