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In layman's terms, Duality principle just says that you replace each and every 'and' with 'or' & vice-versa; every 't (tautology)' with 'c(contradiction)'Suyash Singh said:Homework Statement
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What is dual?
Homework Equations
The Attempt at a Solution
Not on net. Meaning of dual i don't know and can't find.
baldbrain said:In layman's terms, Duality principle just says that you replace each and every 'and' with 'or' & vice-versa; every 't (tautology)' with 'c(contradiction)'
So first you express 'p implies q' in an equivalent form of 'ands' and 'ors', same thing again with the whole expression, and then apply the dual.
Keep in mind that you don't touch the negations (if any) in the expression. For further reading, visit Boolean algebra - Wikipedia.
No, not contrapositive.MidgetDwarf said:Not sure If I understood correctly. Do we just take the contrapositive of this statement? It is the first time I hear the word dual.
or do you mean 'p implies q' is equivalent to not P ∨ Q ?
A dual in the context of truth tables refers to the complement of a logical expression. It is obtained by switching the AND and OR operators and replacing all TRUE values with FALSE and vice versa.
To construct a dual truth table, follow these steps:
Duality in logic and truth tables allows us to switch between AND and OR operations and still maintain the same logical result. This makes it easier to express complex expressions and simplify them using De Morgan's laws.
No, a statement and its dual cannot always be both true. It is possible for a statement and its dual to have different truth values. However, in some cases, they may have the same truth value.
Duality and negation are closely related concepts in logic. Negation is the process of reversing the truth value of a statement, while duality is the process of switching AND and OR operations. By using duality, we can easily express the negation of a logical expression and vice versa.