Equivalències de fórmules booleanes

Llei d’identitat

(A and True)  == A
(A or False)  == A

Llei distributiva

(A and (B or C)) == ((A and B) or (A and C))
(A or (B and C)) == ((A or B) and (A or C))

Lleis de De Morgan

(not (A and B)) == ((not A) or (not B))
(not (A or B))  == ((not A) and (not B))

Doble negació

(not (not A)) == A

Desigualtats

(not (A > B))  == (A <= B)
(not (A < B))  == (A >= B)
(not (A == B)) == (A != B)

Comparar True/False

(A == True)   == A
(A == False)  == (not A)

Propietat commutativa

(A and B) == (B and A)
(A or B)  == (B or A)

Propietat associativa

((A and B) and C) == (A and (B and C))
((A or B)  or C)  == (A or (B or C))