| a + 0 | a | a OR F | a | Identity laws |
| a . 1 | a | a AND T | a | |
| a + 1 | 1 | a OR T | T | |
| a . 0 | 0 | a AND F | F | |
| a + a' | 1 | a OR (NOT a) | T | Complement laws |
| a . a' | 0 | a AND (NOT a) | F | |
| a . (b + c) | a . b + a . c | a AND (b OR c) | (a AND b) OR (a AND c) | Distributive laws |
| a + b . c | (a + b) . (a + c) | a OR (b AND c) | (a OR b) AND (a OR c) | |
| a + b | b + a | a OR b | b OR a | Communicative laws |
| a . b | b . a | a AND b | b AND a | |
| a + b + c | (a + b) + c | a OR b OR c | (a OR b) OR c | Associative laws |
| a + (b + c) | a OR (b OR c) | |||
| a . b . c | a . (b . c) | a AND b AND c | a AND (b AND c) | |
| (a . b) . c | (a AND b) AND c | |||
| (a')' | a | NOT (NOT a) | a | Simplification rules |
| a + a | a | a OR a | a | |
| a . a | a | a AND a | a | |
| a + a . b | a | a OR (a AND b) | a | |
| a . (a + b) | a | a AND (a OR b) | a | |
| a + a' . b | a + b | a OR (NOT a) AND b | a OR b | |
| a . (a' + b) | a . b | a AND ((NOT a) OR b) | a AND b | |
| (a + b + c)' | a' . b' . c' | NOT (a OR b OR c) | (NOT a) AND (NOT b) AND (NOT c) | De Morgan's Theorem |
| (a . b . c)' | a' + b' + c' | NOT (a AND b AND c) | (NOT a) OR (NOT b) OR (NOT c) |
Legend
AND ~ ., another is an upside down V (^) (similar to the upside down U shape used in set theory for an intersection).OR ~ +, another is v (similar to the U shape used in set theory for a union).
NOT ~ ', another is ~.
T ~ 1
F ~ 0
Note Logic and Set theory are just two different ways of tackling the one problem.