[Discrete Mathematics] Fundamental Laws of Boolean Algebra | 불대수의 기본 법칙

Fundamental Laws of Boolean Algebra

불대수의 기본 법칙

* 여기서, \(T\)는 True값을, \(F\)는 False값을 의미한다.

1. Identity Laws (항등법칙)
\(P \land T \iff P\) 
\(P \lor F \iff P\)

2. Domination Laws (지배법칙)
\(P \lor T \iff T\)
\(P \land F \iff F\)

3. Idempotent Laws (멱등법칙)
\(P \lor P \iff P\)
\(P \land P \iff P\)

4. Double Negation Laws (이중부정법칙)
\(\neg (\neg P) \iff P\)

5. Commutative Laws (교환법칙)
\(P \lor Q \iff Q \lor P\)
\(P \land Q \iff Q \land P\)

6. Associative Laws (결합법칙)
\((P \lor Q) \lor R \iff P \lor (Q \lor R)\)
\((P \land Q) \land R \iff P \land (Q \land R)\)

7. Distributive Laws (분배법칙)
\(P \lor (Q \land R) \iff (P \lor Q) \land (P \lor R)\)
\(P \land (Q \lor R) \iff (P \land Q) \lor (P \land R)\)

8. De Morgan's Laws (드모르간 법칙)
\(\neg (P \land Q) \iff \neg P \lor \neg Q\)
\(\neg (P \lor Q) \iff \neg P \land \neg Q\)

9. Implication (함축)
\((P \rightarrow Q) \iff \neg P \lor Q\)

10. Contrapositive (대우)
\((P \rightarrow Q) \iff (\neg Q \rightarrow \neg P)\)