1.1 Prawa algebry Boole'a

A + B = B + A czyli A or B = B or A

AB = BA czyli A and B = B and A

(A + B) + C = A + (B + C) czyli (A or B ) or C = A or ( B or C )

(AB)C = A(BC) czyli (A and B) and C = A and (B and C)

A(B + C) = AB + AC czyli A and ( B or C) = (A and B) or (A and C)

A + (BC) = (A + B)(A + C) czyli A or ( B and C) = (A or B) and (A or C)

A + A = A czyli A or A = A

AA = A czyli A and A = A

znak ¬ to negacja.

AB + A¬B = A czyli (A and B) or (A and not(B))

(A + B) (A + ¬B) = A czyli (A or B) and (A or not(B)) = A

A + AB = A czyli A or (A and B) = A

A(A+B) = A czyli A and (A or B) = A

0 + A = A czyli 0 or A = A

0A = 0 czyli 0 and A = A

1 + A = A czyli 1 or A = A

1A = A czyli 1 and A = A

¬A + A = 1 czyli not(A) or A = 1

¬AA = 0 czyli (not(A) and A) = 0

A + ¬AB = A + B czyli A or (not(A) and B) = A or B

A(¬A + B ) = AB czyli A and (not(A) or B) = A and B

¬(a + b) = ¬a¬b czyli not(A or B) = not(A) and not(B)

¬(AB) = ¬A or ¬B czyli not(A and B) = not(A) or not(B)