Which of the following is valid for Boolean algebra but NOT for ordinary algebra?
Which of the following is valid for Boolean algebra but NOT for ordinary algebra? Correct Answer X + (Y.Z) = (X + Y).(X + Z)
In Boolean algebra:
X + (Y.Z) = (X + Y).(X + Z)
But not true in ordinary algebra:
Example: X = 1, Y = 2 and Z = 3
LHS = X + (Y.Z) = 1 + 2 × 3 = 7
RHS = (1 + 2).(1 + 3) = 3 × 4 = 2
Important Point:
|
Law |
Remark |
|
A + B = B + A |
Commutative Law |
|
A + (B + C) = (A + B) + C |
Associative Law |
|
A (B + C) = AB + AC |
Distributive Law |
|
A + 1 = 1 |
Identity Law/Redundancy Law |
|
A + 0 = A |
|
|
A + A = A |
|
|
A + A̅ = 1 |
|
|
A + AB = A |
Absorption Law |
|
A̅ = A |
Involution Law |
|
A + A̅B = A + B |
- |
|
B̅ + B̅ = B |
Confusion Points
Here Ordinary algebra means simple maths algebra.
Option 2) will include only in boolean algebra. But option 3) is true for both Boolean as well as Maths algebra.
মোঃ আরিফুল ইসলাম
Feb 20, 2025
