Table 2.2
provides the basic Boolean theorems. Each theorem is described by two parts
that are duals of each other.
Principle of duality
1. Interchanging the OR and AND
operations of the expression.
2. Interchanging the 0 and
1 elements of the expression.
3. Not changing the form
of the variables.
Table
2.2 Theorems of Boolean Algebra
-
T1 : Commutative
Law
-
(a) A + B = B + A
(b) A B = B A
-
T2 : Associative
Law
-
(a) (A + B) + C = A + (B + C)
(b) (A B) C = A (B C)
-
T3 : Distributive
Law
-
(a) A (B + C) = A B + A C
(b) A + (B C) = (A + B) (A +
C)
-
T4 : Identity
Law
-
(a) A + A = A
(b) A A = A
-
T5 : Negation
Law
-
(a)
(b) 
-
T6 : Redundance
Law
-
(a) A + A B = A
(b) A (A + B) = A
-
T7 :
-
(a) 0 + A = A
(b) 1 A = A
(c) 1 + A = 1
(d) 0 A = 0
-
T8 :
-
(a)
(b) 
-
T9 :
-
(a)
(b) 
-
T10 : De
Morgan's Theorem
-
(a)
(b) 
The theorems in Table 2.2 can be proved
algebraically, by using the truth tables or by using the Venn diagram.
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