Boolean Logic
Value
True (T)
, False (F)
Operators
, negation, not , conjunction, and , disjunction, or , exclusive or, xor , material implication
Laws
De Morgan's Law
Normal forms
Any complex proposition can be represented by propositions that only include AND, OR as well as NOTs. Given a Boolean Function For each line in its truth table
Then we have
Disjunction Normal Form, DNF
Every -variable proposition can be represented by a disjunction normal form
Conjunction Normal Form, CNF
Similarly, we have
e.g.
This is a natural result of De Morgan's Law
Representation with Least Operators
One could use and only use
- AND, NOT
- OR, NOT
- IMPLICATION to represent all Boolean expressions.