Question

What and Define Equivalent formula or laws of algebra of propositions

Answer 1

If

$\begin{aligned} &p \leftrightarrow q \equiv(p \rightarrow q) \wedge(q \rightarrow p) \\ &p \leftrightarrow q \equiv(p \wedge q) \vee(\neg p \vee \neg p) \end{aligned}$

Then

$\begin{gathered} (\neg p \vee q) \wedge(p \vee \neg q)(\text { Commutation }) \\ (\neg p \vee q) \wedge(\neg q \vee p) \text { (Implication) } \\ (p \rightarrow q) \wedge(q \rightarrow p) \text { (Equivalence) } \\ \qquad \begin{aligned} p & \leftrightarrow q \equiv(\text { Equivalence }) \\ (p \wedge q) & \vee(\neg p \wedge \neg q)(\text { DeMorgan }) \\ (p \wedge q) & \vee \neg(p \vee q)(\text { Commutation }) \\ \neg(p \wedge q) & \vee(p \wedge q)(\text { Implication }) \\ &(p \wedge q) \rightarrow(p \wedge q) \end{aligned} \end{gathered}$