Question
Download Solution PDFIf A = 1 and B = 0, then in terms of Boolean algebra, A + BÌ… =
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
- The branch of algebra that deals with the values of the variables in the form of the truth values i.e., true and false are called Boolean algebra.
- True and false are usually denoted by 1 and 0 respectively.
EXPLANATION:
Given that:
A = 1
B = 0
∴ BÌ… = 1 (Since BÌ… is reverse of B)
A + BÌ… = 1 + 1 = 1 (Since A + A = A)
A + BÌ… = 1 = A
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Boolean Laws |
||
|
Law |
Dual Pair |
Remark |
|
A + B = B + A |
A.B = B.A |
Commutative Law |
|
A + (B + C) = (A + B) + C |
A (BC) = (AB) C |
Associative Law |
|
A (B + C) = AB + AC |
A + (BC) = (A + B) (A + C) |
Distributive Law |
|
A + 1 = 1 |
A.1 = A |
Identity Law/Redundancy Law |
|
A + 0 = A |
A.0 = 0 |
|
|
A + A = A |
A.A = A |
|
|
A + AÌ… = 1 |
A.AÌ… = 0 |
|
|
A + AB = A |
A (A + B) = A |
Absorption Law |
|
\(\overline{\overline A} = A\) |
- |
Involution Law |
|
A + AÌ…B = A + B |
A(AÌ… + B) = A |
- |
|
BÌ… + BÌ… = B |
- |
- |
Last updated on May 31, 2025
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