Truth Tables for the Laws of Boolean
| Boolean Expression | Description | Equivalent Switching Circuit | Boolean Algebra Law or Rule |
| A + 1 = 1 | A in parallel with closed = "CLOSED" |  | Annulment |
| A + 0 = A | A in parallel with open = "A" |  | Identity |
| A . 1 = A | A in series with closed = "A" |  | Identity |
| A . 0 = 0 | A in series with open = "OPEN" |  | Annulment |
| A + A = A | A in parallel with A = "A" |  | Idempotent |
| A . A = A | A in series with A = "A" |  | Idempotent |
| NOT A = A | NOT NOT A (double negative) = "A" | Double Negation | |
| A + A = 1 | A in parallel with NOT A = "CLOSED" |  | Complement |
| A . A = 0 | A in series with NOT A = "OPEN" |  | Complement |
| A+B = B+A | A in parallel with B = B in parallel with A |  | Commutative |
| A.B = B.A | A in series with B = B in series with A |  | Commutative |
| A+B = A.B | invert and replace OR with AND | de Morgan’s Theorem | |
| A.B = A+B | invert and replace AND with OR | de Morgan’s Theorem |
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