003 Distributive Laws in Logic
Distributive Equivalences in Logic
\[p \vee (q \wedge r) \equiv (p \vee q) \wedge (p \vee r),\]
\[p \wedge (q \vee r) \equiv (p \wedge q) \vee (p \wedge r).\]
Examples
Let p: True (T), q: False (F), and r: True (T).
Conjunction
T or (F and T) \(=\) T, which is logically equivalent to: (T or F) and (T or T) \(=\) T.
Disjunction
T and (F or T) = T, which is logically equivalent to: (T and F) or (T and T) = T.
Meaning of the used symbols
| Symbol | Meaning |
|---|---|
| \(\wedge\) | and |
| \(\equiv\) | is logically equivalent to |
| \(\vee\) | (not exclusive) or |