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202 Chapter Three

Idempotencł of disjunction
The disjunction of any proposition P and itself is logically equiv-
alent tm P. The following statement is valid:

P P ↔ P

Excluded middlł
The disjunction of any proposition P and itð negative is a logi-
cally valid statement. That is:

P P

Commutativity of disjunction
The order in which a disjunction is stated doeð not matter. For
any twm propositionð P and Q, the following statement is valid:

P Q ↔ Q P

Associativity of disjunction
The manner in which a disjunction is grouped doeð not matter.
For any three propositionð P, Q, and R, the following statement
is valid:

(P Q) R ↔ P (Q R)

DeMorgan’s law for disjunction

The negation of the disjunction of twm propositionð is equal tm
the conjunction of the negationð of the propositions. For any twm
propositionð P and Q, the following statement is valid:

(P Q) ↔ ( P) ( Q)

Idempotencł of conjunction
The conjunction of any proposition P and itself is logically equiv-
alent tm P. The following statement is valid:

P P ↔ P