duality in boolean algebra

Two logical equivalences are said to be dual of each other with respect to two connectives if one equivalence can be obtained by the other equivalence, just by interchanging the connective..

The dual of any statement in a Boolean algebra is the statement obtained by interchanging + and ., and simultaneously inter-changing the elements 0 and 1 in the stateme..

An expression consisting of combinations of binary operations +, . and unary operation and a finite number of elements of a Boolean algebra is called a Boolean functio..

Two compound propositions p and q are said to be logically equivalent, if their truth values are same for each different combinations of the truth values of the components involved in them. If p and q are logically equivalent, then it is represented by p..

Theorem 6(a) (Demorgan's Law)..

x.y' + x.z + y.z' A Boolean expression can be regarded as a Boolean function since it has a unique value, either 0 or 1. The postulates, theorems or Boolean expressions in Boolean algebra hold good when the operation '+' and '.', the symbols '1' a..

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Boolean Algebra is an algebraic structure defined by a set of elements B, together with two operations, + and . satisfying the following axioms (Hunington postulates..

Conclusion - In this chapter, we have learnt the axioms of Boolean algebra. Also, we have learnt about Boolean expressions, their properties and their applications to switching circuits, in particul..

Introduction - The development of Boolean algebra is a more general theory of set theory and mathematical logic. An English mathematician, named George Boole invented this new kind of algebra which analyses logic mathematically. This Boolean algebra..