Boolean Algebra Cheat Sheet
I previously posted a logic rules cheat sheet and figured it was about time that I do the same for boolean algebra.
| Expression | Equivalent To | Name of the Rule |
|---|---|---|
| $$ X + Y $$ | $$ Y + X $$ | Commutative |
| $$ X \cdot Y $$ | $$ Y \cdot X $$ | Commutative |
| $$ (X + Y) + Z $$ | $$ X + (Y + Z) $$ | Associative |
| $$ (X \cdot Y) \cdot Z $$ | $$ X \cdot (y \cdot Z) $$ | Associative |
| $$ X + (Y \cdot Z) $$ | $$ (X + Y) \cdot (Z + Z) $$ | Distributive |
| $$ X \cdot (Y + Z) $$ | $$ (X \cdot Y) + (X \cdot Z) $$ | Distributive |
| $$ X + 0 $$ | $$ X $$ | Identity |
| $$ X \cdot 1 $$ | $$ X $$ | Identity |
| $$ X + X’ $$ | $$ 1 $$ | Complement |
| $$ X \cdot X’ $$ | $$ 0 $$ | Complement |
| $$ X + X $$ | $$ X $$ | Idempotence |
| $$ X \cdot X $$ | $$ X $$ | Idempotence |