duality


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Duality
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..
Principle of Duality
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 statemen..
Logical Equivalence and Duality
Logical Equivalence and Duality - 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 ..
Logical Equivalence and Duality
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..
Principle of Duality (Contd...)
Theorem 6(a) (Demorgan's Law)..
Example:
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' and '0' are interchanged, this is called principle ..
Matter Waves
/c to photons of energy h u . The elastic scattering of a photon from an electron at rest can be worked out by using the principles of conservation of energy and conservation of momentum. The discovery in 1905 of the dual nature of light was followed by the discovery of dual nature of matter. Even..
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