These are some of the laws of boolean logic they tought me in school. They can be used to simplify complex boolean equations.

The dot (.) means logical and, the + logical or, and the ! is inversion. Forgive me if I get the names of the laws wrong, but I went to a dutch school, so I just translated them.

 AND-Laws                                                  OR-Laws
A = !!A                                 inversion	  A = !!A
A . !A = 0                              1st basic law     A + !A = 1
A . A = A                               2nd basic law     A + A = 1
A . 1 = A                               3rd basic law     A + 1 = 1
A . 0 = 0                               4th basic law     A + 0 = A

A . B = B . A                           commutative       A + B = B + A
A . (A + B) = A                         true absorption   A + (A . B) = A
A . (!A + B) = A . B                    false absorption  A + (!A . B) = A + B
(A + B) . (A + C) = A + (B . C)         distribution      (A . B) + (A . C) = A . (B + C)

A . (B . C) = B . (A . C) = C . (A . B) associative       A + (B + C) = B + (A + C) = C + (A + B)
!(A . B) = !A + !B                      Morgan            !(A + B) = !A . !B

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