Boolean Algebra Laws Cheat Sheet by theTrueEnder

1. X + 0 = X	1D. X·1 = X
2. X + 1 = 1	2D. X·0 = 0

3. X + X = X

3D. X·X = X

4. (X´)´ = X

5. X + X´ = 1

5D. X·X´ = 0

6. X + Y = Y + X

6D. XY = YX

7. (X + Y) + Z = X + (Y + Z) = X + Y + Z

7D. (XY)Z = X(YZ) = XYZ

8. X(Y + Z) = XY + XZ

8D. X + YZ = (X + Y)(X + Z)

9. XY + XY´ = X	9D. (X + Y)(X + Y´) = X
10. X + XY = X	10D. X(X + Y) = X
11. X(X´ + Y) = XY	11D. X + X´Y = X + Y

12. (X + Y + Z + . . .)´ = X´Y´Z´. . .

12D. (XYZ. . .)´ = X´ + Y´ + Z´ + . . .

13. (X + Y + Z)^D = XYZ. . .

13D. (XYZ. . .)^D = X + Y + X + . . .

14. (X + Y)(X´ + Z) = XZ + X´Y

14D. XY + X´Z = (X + Z)(X´ + Y)

15. XY + YZ + X´Z = XY + YZ

15D. (X + Y)(Y + Z)(X´ + Z) = (X + Y)(X´ + Z)

XOR: X @ Y = X´Y + XY´

XNAND: (X @ Y)´ X = Y = X´Y´ + XY