Question
Download Solution PDFLogical expression (A+B) (A+C) is equal to
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven logical expression can be written as:
(A+B) (A+C) = A.A + A.C + B.A + B.C
Since A.A = A, the above expression becomes:
= A + A.C + A.B + B.C
= A(1 + C + B) + B.C
Since 1 + any variable = 1, the above expression becomes:
= A + B.C
(A+B) (A+C) = A + B.C
|
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’ |
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