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$p \land q \equiv q \land p$ and $p \lor q \equiv q \lor p$

$p \lor T \equiv T$ and $p \land F \equiv F$

$p \leftrightarrow q \equiv (p \rightarrow q) \land (q \rightarrow p)$

$p \land (q \lor r) \equiv (p \land q) \lor (p \land r)$ and $p \lor (q \land r) \equiv (p \lor q) \land (p \lor r)$

$\neg (\neg p) \equiv p$

$\neg (p \land q) \equiv \neg p \lor \neg q$ and $\neg (p \lor q) \equiv \neg p \land \neg q$

$p \land p \equiv p$ and $p \lor p \equiv p$

$p \rightarrow q \equiv \neg p \lor q$

$(p \land q) \land r \equiv p \land (q \land r)$ and $(p \lor q) \lor r \equiv p \lor (q \lor r)$

$p \lor \neg p \equiv T$ and $p \land \neg p \equiv F$

$p \land (p \lor q) \equiv p$ and $p \lor (p \land q) \equiv p$