| Name | Conjunction ($\boldsymbol{\wedge}$) version | Disjunction ($\boldsymbol{\vee}$) version |
|---|
| Identity Law | $p \wedge \boldsymbol 1 \Leftrightarrow p$ | $p \vee \boldsymbol 0 \Leftrightarrow p$ |
| Null Law | $p \wedge \boldsymbol 0 \Leftrightarrow \boldsymbol 0$ | $p \vee \boldsymbol 1 \Leftrightarrow \boldsymbol 1$ |
| Idempotent Law | $p \wedge p \Leftrightarrow p$ | $p \vee p \Leftrightarrow p$ |
| Complement Law | $p \wedge \neg p \Leftrightarrow \boldsymbol 0$ | $p \vee \neg p \Leftrightarrow \boldsymbol 1$ |
| Commutative Law | $p \wedge q \Leftrightarrow q \wedge p$ | $p \vee q \Leftrightarrow q \vee p$ |
| Associative Law | $(p \wedge q) \wedge r \Leftrightarrow p \wedge (q \wedge r)$ | $(p \vee q) \vee r \Leftrightarrow p \vee (q \wedge r)$ |
| Distributive Law | $p \vee (q \wedge r) \Leftrightarrow (p \vee q) \wedge (p \vee r)$ | $p \wedge (q \vee r) \Leftrightarrow (p \wedge q) \vee (p \wedge r)$ |
| Absorption Law | $p \wedge (p \vee q ) \Leftrightarrow p$ | $p \vee (p \wedge q) \Leftrightarrow p$ |
| DeMorgan's Law | $p \wedge q \Leftrightarrow \neg(\neg p \vee \neg q)$ | $p \vee q \Leftrightarrow \neg(\neg p \wedge \neg q)$ |
| Double Negation Law | $\neg(\neg p) \Leftrightarrow \neg\neg p \Leftrightarrow p$ |
These notes by Miriam Briskman are licensed under CC BY-NC 4.0 and based on sources.