Basic Electrical and Electronics Engineering: Unit IV: Digital Electronics
Duality Theorem
Properties | Boolean Algebra
The table shows the list theorems of Boolean algebra and four of it postulates.
BASIC
THEOREMS AND PROPERTIES
Duality
1.
A + Ā = 1, since 
2.
A . Ā = 0, since 
The
table shows the list theorems of Boolean algebra and four of it postulates
(i)
A+0 = A
(ii)
A.1 = A
(iii)
A+ Ā = 1
(iv)
A . Ā = 0
(v) A+A = A
(vi)
A . A = A
(vii)
A + 1 = A
(viii)
A . 0 = 0
Ā
= A
Theorem
=A+
AB
=A
(1+B)
=
A.1
=
A
Theorem
A+
ĀB = A+B
⇒ A+ ĀB
⇒ (A + Ā) (A + B)
[Using
distributive law] [A + A = 1]
⇒ 1. (A + B)
A+
ĀB = (A + B)
Theorem
A.(
Ā + B) = AB
A
(Ā + B) ⇒ by using distributive
law (A . Ā) = 0
(A . Ā) + (A.B)
A
. (Ā + B) = AB
Basic Electrical and Electronics Engineering: Unit IV: Digital Electronics : Tag: : Properties | Boolean Algebra - Duality Theorem
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