Question
Download Solution PDFWhat is the result of applying the complement law A + A' in Boolean algebra?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
To understand why the complement law holds, we need to analyze the truth table for the expression A + A'. A truth table lists all possible values of the variables involved and the resulting value of the expression for each combination of variable values. In this case, we are dealing with a single variable A, which can either be 0 or 1.
| A | A' | A + A' |
|---|---|---|
| 0 | 1 | 1 |
| 1 | 0 | 1 |
|
Name |
AND Form |
OR Form |
|
Identity law |
1.A=A |
0+A=A |
|
Null Law |
0.A=0 |
1+A=1 |
|
Idempotent Law |
A.A=A |
A+A=A |
|
Inverse Law |
AA’=0 |
A+A’=1 |
|
Commutative Law |
AB=BA |
A+B=B+A |
|
Associative Law |
(AB)C |
(A+B)+C = A+(B+C) |
|
Distributive Law |
A+BC=(A+B)(A+C) |
A(B+C)=AB+AC |
|
Absorption Law |
A(A+B)=A |
A+AB=A |
|
De Morgan’s Law |
(AB)’=A’+B’ |
(A+B)’=A’B’ |
Last updated on Jun 7, 2025
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